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Unwrapping a Circle: Exploring the Geometry of a Circle

Unwrapping a Circle: Exploring the Geometry of a Circle
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2011-09-13 13:01
CircleGeometric Construction
This example demonstrates how to understand the properties of a circle through geometric construction. Key mathematical concepts include the radius, center, similar triangles, and quadratic equations. Construction involves using GeoGebra commands such as CurveCartesian, Tangent, Circle, and Intersect. Suitable for middle school or high school students to learn geometric construction and circle properties.

GeoGebra Commands & Parameters

  1. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius) → A6
  2. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, 6.28319) → A7
  3. CurveCartesian(radius, t, t, 0, length) → C6
  4. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A10 * length / radius) → B10
  5. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A11 * length / radius) → B11
  6. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A12 * length / radius) → B12
  7. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A13 * length / radius) → B13
  8. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A14 * length / radius) → B14
  9. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A15 * length / radius) → B15
  10. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A16 * length / radius) → B16
  11. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A17 * length / radius) → B17
  12. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A18 * length / radius) → B18
  13. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A9 * length / radius) → B9
  14. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A19 * length / radius) → B19
  15. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A20 * length / radius) → B20
  16. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A21 * length / radius) → B21
  17. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A22 * length / radius) → B22
  18. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A23 * length / radius) → B23
  19. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A24 * length / radius) → B24
  20. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A25 * length / radius) → B25
  21. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A26 * length / radius) → B26
  22. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A27 * length / radius) → B27
  23. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A28 * length / radius) → B28
  24. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A29 * length / radius) → B29
  25. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A30 * length / radius) → B30
  26. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A31 * length / radius) → B31
  27. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A32 * length / radius) → B32
  28. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A33 * length / radius) → B33
  29. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A34 * length / radius) → B34
  30. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A35 * length / radius) → B35
  31. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A36 * length / radius) → B36
  32. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A37 * length / radius) → B37
  33. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A38 * length / radius) → B38
  34. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A39 * length / radius) → B39
  35. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A40 * length / radius) → B40
  36. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A41 * length / radius) → B41
  37. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A42 * length / radius) → B42
  38. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A43 * length / radius) → B43
  39. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A44 * length / radius) → B44
  40. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A45 * length / radius) → B45
  41. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A46 * length / radius) → B46
  42. Tangent(C9, B9) → D9
  43. Tangent(C10, B10) → D10
  44. Tangent(C11, B11) → D11
  45. Tangent(C12, B12) → D12
  46. Tangent(C13, B13) → D13
  47. Tangent(C14, B14) → D14
  48. Tangent(C15, B15) → D15
  49. Tangent(C16, B16) → D16
  50. Tangent(C17, B17) → D17
  51. Tangent(C18, B18) → D18
  52. Tangent(C19, B19) → D19
  53. Tangent(C20, B20) → D20
  54. Tangent(C21, B21) → D21
  55. Tangent(C22, B22) → D22
  56. Tangent(C23, B23) → D23
  57. Tangent(C24, B24) → D24
  58. Tangent(C25, B25) → D25
  59. Tangent(C26, B26) → D26
  60. Tangent(C27, B27) → D27
  61. Tangent(C28, B28) → D28
  62. Tangent(C29, B29) → D29
  63. Tangent(C30, B30) → D30
  64. Tangent(C31, B31) → D31
  65. Tangent(C32, B32) → D32
  66. Tangent(C33, B33) → D33
  67. Tangent(C34, B34) → D34
  68. Tangent(C35, B35) → D35
  69. Circle(C10, A10 * length) → E10
  70. Circle(C11, A11 * length) → E11
  71. Circle(C12, A12 * length) → E12
  72. Circle(C13, A13 * length) → E13
  73. Circle(C14, A14 * length) → E14
  74. Circle(C15, A15 * length) → E15
  75. Circle(C16, A16 * length) → E16
  76. Circle(C17, A17 * length) → E17
  77. Circle(C18, A18 * length) → E18
  78. Circle(C19, A19 * length) → E19
  79. Circle(C20, A20 * length) → E20
  80. Circle(C21, A21 * length) → E21
  81. Circle(C22, A22 * length) → E22
  82. Circle(C23, A23 * length) → E23
  83. Circle(C24, A24 * length) → E24
  84. Circle(C25, A25 * length) → E25
  85. Circle(C26, A26 * length) → E26
  86. Circle(C27, A27 * length) → E27
  87. Circle(C28, A28 * length) → E28
  88. Circle(C29, A29 * length) → E29
  89. Circle(C30, A30 * length) → E30
  90. Circle(C31, A31 * length) → E31
  91. Circle(C32, A32 * length) → E32
  92. Circle(C33, A33 * length) → E33
  93. Circle(C34, A34 * length) → E34
  94. Circle(C35, A35 * length) → E35
  95. Intersect(E10, D10) → F10, G10
  96. Intersect(E11, D11) → F11, G11
  97. Intersect(E12, D12) → F12, G12
  98. Intersect(E13, D13) → F13, G13
  99. Intersect(E14, D14) → F14, G14
  100. Intersect(E15, D15) → F15, G15
  101. Intersect(E16, D16) → F16, G16
  102. Intersect(E17, D17) → F17, G17
  103. Intersect(E18, D18) → F18, G18
  104. Intersect(E19, D19) → F19, G19
  105. Intersect(E20, D20) → F20, G20
  106. Intersect(E21, D21) → F21, G21
  107. Intersect(E22, D22) → F22, G22
  108. Intersect(E23, D23) → F23, G23
  109. Intersect(E24, D24) → F24, G24
  110. Intersect(E25, D25) → F25, G25
  111. Intersect(E26, D26) → F26, G26
  112. Intersect(E27, D27) → F27, G27
  113. Intersect(E28, D28) → F28, G28
  114. Intersect(E29, D29) → F29, G29
  115. Intersect(E30, D30) → F30, G30
  116. Intersect(E31, D31) → F31, G31
  117. Intersect(E32, D32) → F32, G32
  118. Intersect(E33, D33) → F33, G33
  119. Intersect(E34, D34) → F34, G34
  120. Intersect(E35, D35) → F35, G35
  121. Segment(C10, G10) → H10
  122. Segment(C11, G11) → H11
  123. Segment(C12, G12) → H12
  124. Segment(C13, G13) → H13
  125. Segment(C14, G14) → H14
  126. Segment(C15, G15) → H15
  127. Segment(C16, G16) → H16
  128. Segment(C17, G17) → H17
  129. Segment(C18, G18) → H18
  130. Segment(C19, G19) → H19
  131. Segment(C20, G20) → H20
  132. Segment(C21, G21) → H21
  133. Segment(C22, G22) → H22
  134. Segment(C23, G23) → H23
  135. Segment(C24, G24) → H24
  136. Segment(C25, G25) → H25
  137. Segment(C26, G26) → H26
  138. Segment(C27, G27) → H27
  139. Segment(C28, G28) → H28
  140. Segment(C29, G29) → H29
  141. Segment(C30, G30) → H30
  142. Segment(C31, G31) → H31
  143. Segment(C32, G32) → H32
  144. Segment(C33, G33) → H33
  145. Segment(C34, G34) → H34
  146. Segment(C35, G35) → H35
  147. Tangent(C36, B36) → D36
  148. Tangent(C37, B37) → D37
  149. Tangent(C38, B38) → D38
  150. Tangent(C39, B39) → D39
  151. Tangent(C40, B40) → D40
  152. Tangent(C41, B41) → D41
  153. Tangent(C42, B42) → D42
  154. Tangent(C43, B43) → D43
  155. Tangent(C44, B44) → D44
  156. Tangent(C45, B45) → D45
  157. Tangent(C46, B46) → D46
  158. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A47 * length / radius) → B47
  159. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A48 * length / radius) → B48
  160. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A49 * length / radius) → B49
  161. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A50 * length / radius) → B50
  162. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A51 * length / radius) → B51
  163. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A52 * length / radius) → B52
  164. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A53 * length / radius) → B53
  165. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A54 * length / radius) → B54
  166. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A55 * length / radius) → B55
  167. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A56 * length / radius) → B56
  168. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A57 * length / radius) → B57
  169. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A58 * length / radius) → B58
  170. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A59 * length / radius) → B59
  171. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A60 * length / radius) → B60
  172. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A61 * length / radius) → B61
  173. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A62 * length / radius) → B62
  174. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A63 * length / radius) → B63
  175. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A64 * length / radius) → B64
  176. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A65 * length / radius) → B65
  177. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A66 * length / radius) → B66
  178. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A67 * length / radius) → B67
  179. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A68 * length / radius) → B68
  180. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A69 * length / radius) → B69
  181. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A70 * length / radius) → B70
  182. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A71 * length / radius) → B71
  183. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A72 * length / radius) → B72
  184. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A73 * length / radius) → B73
  185. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A74 * length / radius) → B74
  186. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A75 * length / radius) → B75
  187. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A76 * length / radius) → B76
  188. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A77 * length / radius) → B77
  189. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A78 * length / radius) → B78
  190. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A79 * length / radius) → B79
  191. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A80 * length / radius) → B80
  192. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A81 * length / radius) → B81
  193. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A82 * length / radius) → B82
  194. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A83 * length / radius) → B83
  195. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A84 * length / radius) → B84
  196. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A85 * length / radius) → B85
  197. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A86 * length / radius) → B86
  198. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A87 * length / radius) → B87
  199. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A88 * length / radius) → B88
  200. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A89 * length / radius) → B89
  201. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A90 * length / radius) → B90
  202. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A91 * length / radius) → B91
  203. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A92 * length / radius) → B92
  204. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A93 * length / radius) → B93
  205. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A94 * length / radius) → B94
  206. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A95 * length / radius) → B95
  207. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A96 * length / radius) → B96
  208. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A97 * length / radius) → B97
  209. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A98 * length / radius) → B98
  210. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A99 * length / radius) → B99
  211. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A100 * length / radius) → B100
  212. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A101 * length / radius) → B101
  213. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A102 * length / radius) → B102
  214. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A103 * length / radius) → B103
  215. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A104 * length / radius) → B104
  216. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A105 * length / radius) → B105
  217. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A106 * length / radius) → B106
  218. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A107 * length / radius) → B107
  219. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A108 * length / radius) → B108
  220. CurveCartesian(radius * cos(t), radius * sin(t), t, 0, length / radius - A109 * length / radius) → B109
  221. Tangent(C47, B47) → D47
  222. Tangent(C48, B48) → D48
  223. Tangent(C49, B49) → D49
  224. Tangent(C50, B50) → D50
  225. Tangent(C51, B51) → D51
  226. Tangent(C52, B52) → D52
  227. Tangent(C53, B53) → D53
  228. Tangent(C54, B54) → D54
  229. Tangent(C55, B55) → D55
  230. Tangent(C56, B56) → D56
  231. Tangent(C57, B57) → D57
  232. Tangent(C58, B58) → D58
  233. Tangent(C59, B59) → D59
  234. Tangent(C60, B60) → D60
  235. Tangent(C61, B61) → D61
  236. Tangent(C62, B62) → D62
  237. Tangent(C63, B63) → D63
  238. Tangent(C64, B64) → D64
  239. Tangent(C65, B65) → D65
  240. Tangent(C66, B66) → D66
  241. Tangent(C67, B67) → D67
  242. Tangent(C68, B68) → D68
  243. Tangent(C69, B69) → D69
  244. Tangent(C70, B70) → D70
  245. Tangent(C71, B71) → D71
  246. Tangent(C72, B72) → D72
  247. Tangent(C73, B73) → D73
  248. Tangent(C74, B74) → D74
  249. Tangent(C75, B75) → D75
  250. Tangent(C76, B76) → D76
  251. Tangent(C77, B77) → D77
  252. Tangent(C78, B78) → D78
  253. Tangent(C79, B79) → D79
  254. Tangent(C80, B80) → D80
  255. Tangent(C81, B81) → D81
  256. Tangent(C82, B82) → D82
  257. Tangent(C83, B83) → D83
  258. Tangent(C84, B84) → D84
  259. Tangent(C85, B85) → D85
  260. Tangent(C86, B86) → D86
  261. Tangent(C87, B87) → D87
  262. Tangent(C88, B88) → D88
  263. Tangent(C89, B89) → D89
  264. Tangent(C90, B90) → D90
  265. Tangent(C91, B91) → D91
  266. Tangent(C92, B92) → D92
  267. Tangent(C93, B93) → D93
  268. Tangent(C94, B94) → D94
  269. Tangent(C95, B95) → D95
  270. Tangent(C96, B96) → D96
  271. Tangent(C97, B97) → D97
  272. Tangent(C98, B98) → D98
  273. Tangent(C99, B99) → D99
  274. Tangent(C100, B100) → D100
  275. Tangent(C101, B101) → D101
  276. Tangent(C102, B102) → D102
  277. Tangent(C103, B103) → D103
  278. Tangent(C104, B104) → D104
  279. Tangent(C105, B105) → D105
  280. Tangent(C106, B106) → D106
  281. Tangent(C107, B107) → D107
  282. Tangent(C108, B108) → D108
  283. Circle(C36, A36 * length) → E36
  284. Circle(C37, A37 * length) → E37
  285. Circle(C38, A38 * length) → E38
  286. Circle(C39, A39 * length) → E39
  287. Circle(C40, A40 * length) → E40
  288. Circle(C41, A41 * length) → E41
  289. Circle(C42, A42 * length) → E42
  290. Circle(C43, A43 * length) → E43
  291. Circle(C44, A44 * length) → E44
  292. Circle(C45, A45 * length) → E45
  293. Circle(C46, A46 * length) → E46
  294. Circle(C47, A47 * length) → E47
  295. Circle(C48, A48 * length) → E48
  296. Circle(C49, A49 * length) → E49
  297. Circle(C50, A50 * length) → E50
  298. Circle(C51, A51 * length) → E51
  299. Circle(C52, A52 * length) → E52
  300. Circle(C53, A53 * length) → E53
  301. Circle(C54, A54 * length) → E54
  302. Circle(C55, A55 * length) → E55
  303. Circle(C56, A56 * length) → E56
  304. Circle(C57, A57 * length) → E57
  305. Circle(C58, A58 * length) → E58
  306. Circle(C59, A59 * length) → E59
  307. Circle(C60, A60 * length) → E60
  308. Circle(C61, A61 * length) → E61
  309. Circle(C62, A62 * length) → E62
  310. Circle(C63, A63 * length) → E63
  311. Circle(C64, A64 * length) → E64
  312. Circle(C65, A65 * length) → E65
  313. Circle(C66, A66 * length) → E66
  314. Circle(C67, A67 * length) → E67
  315. Circle(C68, A68 * length) → E68
  316. Circle(C69, A69 * length) → E69
  317. Circle(C70, A70 * length) → E70
  318. Circle(C71, A71 * length) → E71
  319. Circle(C72, A72 * length) → E72
  320. Circle(C73, A73 * length) → E73
  321. Circle(C74, A74 * length) → E74
  322. Circle(C75, A75 * length) → E75
  323. Circle(C76, A76 * length) → E76
  324. Circle(C77, A77 * length) → E77
  325. Circle(C78, A78 * length) → E78
  326. Circle(C79, A79 * length) → E79
  327. Circle(C80, A80 * length) → E80
  328. Circle(C81, A81 * length) → E81
  329. Circle(C82, A82 * length) → E82
  330. Circle(C83, A83 * length) → E83
  331. Circle(C84, A84 * length) → E84
  332. Circle(C85, A85 * length) → E85
  333. Circle(C86, A86 * length) → E86
  334. Circle(C87, A87 * length) → E87
  335. Circle(C88, A88 * length) → E88
  336. Circle(C89, A89 * length) → E89
  337. Circle(C90, A90 * length) → E90
  338. Circle(C91, A91 * length) → E91
  339. Circle(C92, A92 * length) → E92
  340. Circle(C93, A93 * length) → E93
  341. Circle(C94, A94 * length) → E94
  342. Circle(C95, A95 * length) → E95
  343. Circle(C96, A96 * length) → E96
  344. Circle(C97, A97 * length) → E97
  345. Circle(C98, A98 * length) → E98
  346. Circle(C99, A99 * length) → E99
  347. Circle(C100, A100 * length) → E100
  348. Circle(C101, A101 * length) → E101
  349. Circle(C102, A102 * length) → E102
  350. Circle(C103, A103 * length) → E103
  351. Circle(C104, A104 * length) → E104
  352. Circle(C105, A105 * length) → E105
  353. Circle(C106, A106 * length) → E106
  354. Circle(C107, A107 * length) → E107
  355. Circle(C108, A108 * length) → E108
  356. Intersect(E36, D36) → F36, G36
  357. Intersect(E37, D37) → F37, G37
  358. Intersect(E38, D38) → F38, G38
  359. Intersect(E39, D39) → F39, G39
  360. Intersect(E40, D40) → F40, G40
  361. Intersect(E41, D41) → F41, G41
  362. Intersect(E42, D42) → F42, G42
  363. Intersect(E43, D43) → F43, G43
  364. Intersect(E44, D44) → F44, G44
  365. Intersect(E45, D45) → F45, G45
  366. Intersect(E46, D46) → F46, G46
  367. Intersect(E47, D47) → F47, G47
  368. Intersect(E48, D48) → F48, G48
  369. Intersect(E49, D49) → F49, G49
  370. Intersect(E50, D50) → F50, G50
  371. Intersect(E51, D51) → F51, G51
  372. Intersect(E52, D52) → F52, G52
  373. Intersect(E53, D53) → F53, G53
  374. Intersect(E54, D54) → F54, G54
  375. Intersect(E55, D55) → F55, G55
  376. Intersect(E56, D56) → F56, G56
  377. Intersect(E57, D57) → F57, G57
  378. Intersect(E58, D58) → F58, G58
  379. Intersect(E59, D59) → F59, G59
  380. Intersect(E60, D60) → F60, G60
  381. Intersect(E61, D61) → F61, G61
  382. Intersect(E62, D62) → F62, G62
  383. Intersect(E63, D63) → F63, G63
  384. Intersect(E64, D64) → F64, G64
  385. Intersect(E65, D65) → F65, G65
  386. Intersect(E66, D66) → F66, G66
  387. Intersect(E67, D67) → F67, G67
  388. Intersect(E68, D68) → F68, G68
  389. Intersect(E69, D69) → F69, G69
  390. Intersect(E70, D70) → F70, G70
  391. Intersect(E71, D71) → F71, G71
  392. Intersect(E72, D72) → F72, G72
  393. Intersect(E73, D73) → F73, G73
  394. Intersect(E74, D74) → F74, G74
  395. Intersect(E75, D75) → F75, G75
  396. Intersect(E76, D76) → F76, G76
  397. Intersect(E77, D77) → F77, G77
  398. Intersect(E78, D78) → F78, G78
  399. Intersect(E79, D79) → F79, G79
  400. Intersect(E80, D80) → F80, G80
  401. Intersect(E81, D81) → F81, G81
  402. Intersect(E82, D82) → F82, G82
  403. Intersect(E83, D83) → F83, G83
  404. Intersect(E84, D84) → F84, G84
  405. Intersect(E85, D85) → F85, G85
  406. Intersect(E86, D86) → F86, G86
  407. Intersect(E87, D87) → F87, G87
  408. Intersect(E88, D88) → F88, G88
  409. Intersect(E89, D89) → F89, G89
  410. Intersect(E90, D90) → F90, G90
  411. Intersect(E91, D91) → F91, G91
  412. Intersect(E92, D92) → F92, G92
  413. Intersect(E93, D93) → F93, G93
  414. Intersect(E94, D94) → F94, G94
  415. Intersect(E95, D95) → F95, G95
  416. Intersect(E96, D96) → F96, G96
  417. Intersect(E97, D97) → F97, G97
  418. Intersect(E98, D98) → F98, G98
  419. Intersect(E99, D99) → F99, G99
  420. Intersect(E100, D100) → F100, G100
  421. Intersect(E101, D101) → F101, G101
  422. Intersect(E102, D102) → F102, G102
  423. Intersect(E103, D103) → F103, G103
  424. Intersect(E104, D104) → F104, G104
  425. Intersect(E105, D105) → F105, G105
  426. Intersect(E106, D106) → F106, G106
  427. Intersect(E107, D107) → F107, G107
  428. Intersect(E108, D108) → F108, G108
  429. Segment(C36, G36) → H36
  430. Segment(C37, G37) → H37
  431. Segment(C38, G38) → H38
  432. Segment(C39, G39) → H39
  433. Segment(C40, G40) → H40
  434. Segment(C41, G41) → H41
  435. Segment(C42, G42) → H42
  436. Segment(C43, G43) → H43
  437. Segment(C44, G44) → H44
  438. Segment(C45, G45) → H45
  439. Segment(C46, G46) → H46
  440. Segment(C47, G47) → H47
  441. Segment(C48, G48) → H48
  442. Segment(C49, G49) → H49
  443. Segment(C50, G50) → H50
  444. Segment(C51, G51) → H51
  445. Segment(C52, G52) → H52
  446. Segment(C53, G53) → H53
  447. Segment(C54, G54) → H54
  448. Segment(C55, G55) → H55
  449. Segment(C56, G56) → H56
  450. Segment(C57, G57) → H57
  451. Segment(C58, G58) → H58
  452. Segment(C59, G59) → H59
  453. Segment(C60, G60) → H60
  454. Segment(C61, G61) → H61
  455. Segment(C62, G62) → H62
  456. Segment(C63, G63) → H63
  457. Segment(C64, G64) → H64
  458. Segment(C65, G65) → H65
  459. Segment(C66, G66) → H66
  460. Segment(C67, G67) → H67
  461. Segment(C68, G68) → H68
  462. Segment(C69, G69) → H69
  463. Segment(C70, G70) → H70
  464. Segment(C71, G71) → H71
  465. Segment(C72, G72) → H72
  466. Segment(C73, G73) → H73
  467. Segment(C74, G74) → H74
  468. Segment(C75, G75) → H75
  469. Segment(C76, G76) → H76
  470. Segment(C77, G77) → H77
  471. Segment(C78, G78) → H78
  472. Segment(C79, G79) → H79
  473. Segment(C80, G80) → H80
  474. Segment(C81, G81) → H81
  475. Segment(C82, G82) → H82
  476. Segment(C83, G83) → H83
  477. Segment(C84, G84) → H84
  478. Segment(C85, G85) → H85
  479. Segment(C86, G86) → H86
  480. Segment(C87, G87) → H87
  481. Segment(C88, G88) → H88
  482. Segment(C89, G89) → H89
  483. Segment(C90, G90) → H90
  484. Segment(C91, G91) → H91
  485. Segment(C92, G92) → H92
  486. Segment(C93, G93) → H93
  487. Segment(C94, G94) → H94
  488. Segment(C95, G95) → H95
  489. Segment(C96, G96) → H96
  490. Segment(C97, G97) → H97
  491. Segment(C98, G98) → H98
  492. Segment(C99, G99) → H99
  493. Segment(C100, G100) → H100
  494. Segment(C101, G101) → H101
  495. Segment(C102, G102) → H102
  496. Segment(C103, G103) → H103
  497. Segment(C104, G104) → H104
  498. Segment(C105, G105) → H105
  499. Segment(C106, G106) → H106
  500. Segment(C107, G107) → H107
  501. Segment(C108, G108) → H108
  502. CurveCartesian(radius + 1, t, t, 0, 2 * 3.141592653589793 * radius) → D6
  503. Segment(J10, (x(J10) - 0.5 * radius, y(J10))) → K10
  504. Segment(J11, (x(J11) - 0.5 * radius, y(J11))) → K11
  505. Segment(J12, (x(J12) - 0.5 * radius, y(J12))) → K12
  506. Segment(J13, (x(J13) - 0.5 * radius, y(J13))) → K13
  507. Segment(J14, (x(J14) - 0.5 * radius, y(J14))) → K14
  508. Segment(J15, (x(J15) - 0.5 * radius, y(J15))) → K15
  509. Segment(J17, (x(J17) - radius, y(J17))) → K17
  510. Segment(J18, (x(J18) - radius, y(J18))) → K18
  511. Segment(J19, (x(J19) - radius, y(J19))) → K19
  512. Segment(J20, (x(J20) - radius, y(J20))) → K20
  513. Angle(A, B, A3) → α
  514. Segment(B, A3) → c