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Proof of Law of Cosines (Using Circle)

Proof of Law of Cosines (Using Circle)
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2020-02-26 03:37
CircleTrigonometryGeometric Construction
This example demonstrates the proof of the Law of Cosines using a circle. It shows how to derive the Law of Cosines by utilizing the properties of the circle and angle relationships. The construction involves commands such as Intersect, Point, Polygon, Angle, Circle, Line, and Segment. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Polygon(B, C, A) → t1, b, c, a
  4. Angle(C, B, A) → θ
  5. Circle(A, B) → d
  6. Line(A, B) → f
  7. Intersect(d, f, 2) → D
  8. Line(B, C) → g
  9. Intersect(d, g, 2) → E
  10. Segment(D, E) → h
  11. Segment(D, B) → i
  12. Segment(B, E) → j
  13. Line(A, C) → l
  14. Intersect(d, l, 2) → F
  15. Intersect(d, l, 1) → G
  16. Segment(G, F) → m

AI Drawing Prompt Reference

Draw a right triangle with a circle centered at the right angle vertex, radius reaching to a point on one of the legs. Draw a perpendicular from the right angle vertex to the hypotenuse, intersecting the circle at two points. Connect these points to the right angle vertex, forming two smaller triangles. Measure the angle and display the lengths of the segments to prove the Law of Cosines.
The prompt above was compiled from the original drawing commands and is for reference only.