MathPlotAI Logo MathPlotAI

Circle Tangent Line | Euclid's Theorem Demonstration

Circle Tangent Line | Euclid's Theorem Demonstration
Loading the math board and drawing, please wait…
2020-12-04 15:28
CircleAngleGeometric Construction
This example demonstrates how to draw a tangent line to a circle and verify Euclid's theorem using GeoGebra. Key math concepts include circle, tangent line, similarity transformation, and geometric construction. Construction highlights involve using GeoGebra commands and objects like Intersect (intersection), Point (point), Circle (circle), Segment (segment), Line (line), OrthogonalLine (perpendicular line), and Angle (angle). Suitable for high school and above learners to understand geometric constructions and theorem verification.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → S
  2. Point(xAxis) → B
  3. Circle(S, B) → k
  4. Point(xAxis) → A
  5. Point(k) → H
  6. Segment(S, H) → f
  7. Segment(H, A) → g
  8. Segment(A, S) → h
  9. Intersect(k, h, 1) → T'
  10. Line(T', g) → u
  11. Intersect(u, f) → F
  12. Segment(F, T') → m
  13. Circle(S, F) → d
  14. Intersect(d, h, 1) → E
  15. Segment(S, B) → l
  16. OrthogonalLine(E, h) → s
  17. Angle(h, s) → α
  18. Intersect(k, s, 1) → T
  19. Line(T, A) → t
  20. Segment(S, T) → r

AI Drawing Prompt Reference

Draw a circle with center S and radius passing through point B. Take point A on the circle, connect SA and AH, and let AH intersect the circle at point H. Connect SH and HA, and let them intersect the circle at point T'. Draw a perpendicular line to HA through T', let it intersect SH at point F. Draw a circle with radius SF, and let it intersect HA at point E. Connect SE and SB, draw a perpendicular line to HA through E, let it intersect HA at point T, and draw a line through T and A, letting it intersect SE at point R.
The prompt above was compiled from the original drawing commands and is for reference only.