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Circle and Segments in a Right Triangle

Circle and Segments in a Right Triangle
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2017-05-11 22:37
TriangleCircleCoordinate GeometryGeometric Construction
This example demonstrates the relationship between a circle and segments in a right triangle. Key concepts include circle, right triangle, segments, and ratios. Using GeoGebra commands such as Circle, Intersect, and Polygon, one can construct a circle and segments in a right triangle. Suitable for students at the junior high school level and above, focusing on coordinate geometry and geometric construction.

GeoGebra Commands & Parameters

  1. Circle(B, C) → c
  2. Point(c) → A
  3. Circle(A, B) → d
  4. Intersect(c, d, 1) → D
  5. Intersect(c, d, 2) → E
  6. Circle(D, A) → e
  7. Circle(E, A) → f
  8. Intersect(c, e, 2) → G
  9. Intersect(c, f, 2) → H
  10. Intersect(d, e, 2) → I
  11. Circle(G, D) → g
  12. Circle(H, E) → h
  13. Intersect(g, h, 2) → F
  14. Circle(F, B) → k
  15. Polygon(A, G, H) → poly1, h_1, a, g_1
  16. Polygon(F, E, D) → poly2, d_1, f_1, e_1