Explore Geometric Relationships with Dragging Points and Slider

GeoGebra Commands & Parameters

1. Point(xAxis) → A
2. Intersect(xAxis, yAxis) → B
3. CircleArc(B, D, A) → c
4. Point(c) → E
5. Polygon(A, E, 4) → poly1, a, b, d, e, F, G
6. Polygon(E, C, 4) → poly2, f, g, h, i, H, I
7. Polygon(C, A, 4) → poly3, j, k, l, m, J, K
8. Polygon(A, E, C) → poly4, c_1, a_1, e_1
9. Midpoint(A, K) → L
10. If(n < 1, n, 1) → r1
11. Rotate(A, (-(((r1 * 180))°)), L) → A'
12. Rotate(E, (-(((r1 * 180))°)), L) → E'
13. Rotate(C, (-(((r1 * 180))°)), L) → C'
14. Polygon(A', E', C') → poly4', c', a', e'
15. If(1 < n < 2, 2 - n, If[n ≥ 2, 0, 1]) → d1
16. Dilate(C, d1, I) → C'_1
17. Dilate(A, d1, F) → A'_1
18. Polygon(A'_1, E, C'_1) → poly5, c'_1, a'_1, e_2
19. Polygon(E, E', K, C) → poly6, e_3, e'_1, k_1, c_2
20. Polygon(E, A, J, E') → poly7, e_4, a_2, j_1, e'_2
21. If(3 < n < 4, n - 3, 1) → r2
22. Rotate(E, ((r2 * 90))°, A) → E'_1
23. Rotate(A, ((r2 * 90))°, A) → A'_2
24. Rotate(J, ((r2 * 90))°, A) → J'
25. Rotate(E', ((r2 * 90))°, A) → E''
26. Polygon(E'_1, A'_2, J', E'') → poly7', e'_3, a'_2, j', e''
27. OrthogonalLine(L, e_3) → p
28. Mirror(C, p) → C'_2
29. Mirror(K, p) → K'
30. If(4 < n < 5, 5 - n, If[n ≥ 5, 0, 1]) → d2
31. Dilate(E, d2, E') → E'_2
32. Dilate(E', d2, E) → E''_1
33. Dilate(C, d2, C'_2) → C'_3
34. Dilate(K, d2, K') → K'_1
35. Polygon(E'_2, C'_3, K'_1, E''_1) → poly8, e'_4, c'_3, k'_1, e''_1
36. If(5 < n < 6, n - 5, 1) → r3
37. Rotate(E'_2, ((r3 * 90))°, A) → M
38. Rotate(C'_3, ((r3 * 90))°, A) → N
39. Rotate(K'_1, ((r3 * 90))°, A) → O
40. Rotate(E''_1, ((r3 * 90))°, A) → P
41. Polygon(M, N, O, P) → poly8', m_1, n_1, o, p_1
42. Line(G, H) → q
43. OrthogonalLine(E, q) → r