MathPlotAI Logo MathPlotAI

Extended Law of Sines by Steve Phelps

Extended Law of Sines by Steve Phelps
Loading the math board and drawing, please wait…
2014-12-26 22:39
TriangleCircleTrigonometry
This example illustrates the Extended Law of Sines, which relates the radius of a triangle's circumcircle to an angle and its opposite side. Using GeoGebra commands such as Circle, CircumcircleArc, and others, it provides a visual demonstration of the properties of a triangle's circumcircle. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Circle(O, 4) → c
  2. Point(c) → E
  3. Point(c) → B
  4. Mirror(B, O) → B'
  5. CircumcircleArc(B, E, B') → h
  6. Point(c) → C
  7. Segment(B, C) → a
  8. Point(h) → A
  9. Segment(C, A) → b
  10. Segment(A, B) → d
  11. Segment(B, O) → e
  12. Segment(O, C) → f
  13. Midpoint(a) → D
  14. Segment(O, D) → g
  15. Angle(B, A, C) → α
  16. Angle(B, O, D) → β
  17. Angle(A, C, B) → δ

AI Drawing Prompt Reference

Draw a triangle ABC with point O as the circumcenter, points E, B, B' on circle c with radius 4. Draw sides a, b, d of the triangle and the perpendicular bisector g from O to D. Measure angles α, β, and δ to show the triangle ABC and its circumcircle with related segments.
The prompt above was compiled from the original drawing commands and is for reference only.