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Van Schooten's Theorem: A Geometric Proof

Van Schooten's Theorem: A Geometric Proof
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2020-03-25 20:39
TriangleCircleGeometric Construction
This example demonstrates the geometric proof of Van Schooten's theorem. Key mathematical concepts include circles, equilateral triangles, and tangents. Using GeoGebra commands such as Intersect, Point, Polygon, etc., the construction involves circles and triangles. Suitable for middle school and above students to learn geometric proofs and properties of circles.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A_1
  2. Point(xAxis) → A_2
  3. Polygon(A_1, A_2, 3) → poly1, f, g, h, A_3
  4. Mirror(O, f) → O'
  5. CircumcircleArc(A_1, O', A_2) → d
  6. Circle(A_1, A_2, A_3) → c_1
  7. Point(d) → P
  8. Segment(P, A_3) → c
  9. Segment(P, A_1) → a
  10. Segment(P, A_2) → b
  11. Rotate(P, 120°, O) → P'
  12. Rotate(A_3, 120°, O) → A
  13. Segment(P', A) → c'
  14. Angle(c', c) → α
  15. Rotate(P, 120°, O) → P''
  16. Rotate(A_2, 120°, O) → B
  17. Segment(P'', B) → b'
  18. Angle(c', b') → β
  19. Intersect(c, c') → C
  20. Angle(C, P, A_1) → γ
  21. Polygon(A_1, C, P) → t1, p, a_1, c_2
  22. Polygon(C, P', A_3) → t2, a_3, c_3, p'_1