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Tangent Secant Theorem Proof Using Similar Triangles

Tangent Secant Theorem Proof Using Similar Triangles
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2015-07-02 21:09
TriangleCircleAngleGeometric Construction
This example demonstrates the proof of the Tangent-Secant Theorem using similar triangles. It involves core mathematical concepts such as similar triangles, circles, angles, and segment length relationships. The construction is achieved using GeoGebra commands like Circle, Tangent, Intersect, Segment, Point, and Angle. It is suitable for high school students learning geometric theorem proofs and serves as an educational aid.

GeoGebra Commands & Parameters

  1. Circle(B_1, Radius) → c
  2. Tangent(B, c) → a, b
  3. Intersect(c, b, 1) → A
  4. Segment(B, A) → AB
  5. Point(c) → C
  6. Segment(B, C) → BC
  7. Intersect(c, BC, 2) → D
  8. Segment(D, A) → f
  9. Segment(A, C) → g
  10. Angle(B, A, D) → AngleBAD
  11. Angle(A, C, B) → AngleBCA
  12. Angle(D, B, A) → AngleABD
  13. Segment(B, D) → BD

AI Drawing Prompt Reference

Draw a circle with center B and any radius. Draw two tangents a and b from B. Let a intersect the circle at A and connect BA. Choose a point C on the circle, draw line BC and extend it to intersect the circle at D. Draw lines AD and AC, and measure the angles BAD, BCA, and ABD.
The prompt above was compiled from the original drawing commands and is for reference only.