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Inscribed Angle Theorem: What Do You See?

Inscribed Angle Theorem: What Do You See?
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2015-10-13 08:10
CircleAngleGeometric Construction
This applet dynamically demonstrates the inscribed angle theorem, which states that the measure of an inscribed angle is half the measure of the arc it intercepts. By dragging points and observing angle changes, students can discover this geometric principle. The construction uses basic objects like circles, arcs, and segments, suitable for middle school and above students.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Segment(B, A) → a
  3. Point(c) → C
  4. Segment(A, C) → b
  5. Point(c) → D
  6. CircumcircleArc(C, D, B) → d
  7. CircleArc(A, B, C) → e
  8. Point(d) → E
  9. Segment(C, E) → f
  10. Segment(E, B) → g
  11. Circle(E, 1.5) → h
  12. Ray(E, C) → i
  13. Ray(E, B) → j
  14. Intersect(h, j) → F,
  15. Intersect(h, i) → G,
  16. CircleSector(E, F, G) → k
  17. Segment(E, A) → l
  18. Line(A, xAxis) → m
  19. Dilate(E, If[0 ≤ n ≤ 1, 1 - n, 0], A) → E'
  20. Vector(E, E') → u
  21. Translate(k, u) → k'
  22. Line(E, a) → p
  23. Line(E, b) → q
  24. Intersect(h, p, 1) → H
  25. Angle(H, E, B) → α
  26. Intersect(h, q, 2) → I
  27. Angle(C, E, I) → β
  28. Dilate(E, If[1 < n ≤ 2, 2 - n, 0], A) → E'_1
  29. Vector(E, E'_1) → v
  30. Translate(k, v) → k'_1
  31. Rotate(k'_1, If[1 < n ≤ 2, ((n - 1) * β), β], E'_1) → k''
  32. Rotate(k', If[0 < n ≤ 1, ((-n) * α), (-α)], E') → k''_1
  33. Circle(A, 1.5) → r
  34. Intersect(r, a, 1) → J
  35. Intersect(r, b, 1) → K
  36. CircleSector(A, J, K) → s

AI Drawing Prompt Reference

Draw a circle and select three points A, B, and C on it. Connect A and B to form a diameter, and connect A and C to form a chord. With B as the center and C as the starting point, draw an arc. With A as the center and C as the starting point, draw another arc. Select a point D on the arc and connect C and D. With C as the center, draw a circle with a radius of 1.5, and draw two rays from C that intersect this circle at points E and F. Connect E and F, and with E as the center, draw a circle with a radius of 1.5, and draw two rays from E that intersect this circle at points G and H. Connect E and H, and with E as the center, draw a circle with a radius of 1.5, and draw two rays from E that intersect this circle at points I and J. Connect E and J, and with E as the center, draw a circle with a radius of 1.5, and draw two rays from E that intersect this circle at points K and L. Connect E and K.
The prompt above was compiled from the original drawing commands and is for reference only.