Question

Let A0.A1,A2,A3,A4 devide a unit circle (circle of radius one) into five equal parts. Prove that the chords A0 A1, A0 A2 satisfy:

(A0 A1 * A0 A2)^2 = 5.

Answer 1

Consider a circle with radius r and center O.

Since A0, A1, A2, A3, A4 devide this unit circle into five equal parts.

Hence radius (r) = 1

Now consider the two chords A0A1 and A0A2.

Using Cosine rule in triangle OA0A1,

_____(1)

Using Cosine rule in triangle OA0A2,

Put value of from eq.(1) ---

Put