MathPlotAI Logo MathPlotAI

Proof of the Sine Rule

Proof of the Sine Rule
Loading the math board and drawing, please wait…
2019-04-15 09:51
TriangleCircleAngleTrigonometryGeometric Construction
In collections MA440
This example demonstrates a simple proof of the sine rule using circle theorems. It involves core math concepts like triangles, circle theorems, and sine functions. Constructed using GeoGebra commands and objects such as Circle, Point, Segment, Angle, Ray, and Intersect. Suitable for high school students learning about the proof of the sine rule.

GeoGebra Commands & Parameters

  1. Circle(O, B) → E
  2. Point(E) → C
  3. Point(E) → A
  4. Segment(A, B) → c
  5. Segment(A, C) → b
  6. Segment(C, B) → a
  7. Angle(C, A, B) → α
  8. Ray(C, O) → d
  9. Intersect(E, d, 2) → D
  10. Segment(C, D) → e
  11. Segment(D, B) → f
  12. Angle(C, D, B) → β
  13. Angle(D, B, C) → γ

AI Drawing Prompt Reference

Draw a circle with center O. Place three points A, B, and C on the circle, ensuring they are not collinear. Connect A, B, and C to form a triangle, and label the angle at A (angle CAB) as α. From point C, draw a ray through the center O, intersecting the circle again at point D. Connect C to D and D to B, forming triangle CDB. Label angle CDB as β and angle DBC as γ. The figure shows triangle ABC inscribed in the circle, with the diameter CD constructed to illustrate the sine rule via circle theorems.
The prompt above was compiled from the original drawing commands and is for reference only.