Let  $A_0 A_1 A_2 A_3 A_4 A_5 $ be a regular hexagon inscribed in a circle of unit radius…

Problem: Let  $A_0 A_1 A_2 A_3 A_4 A_5 $ be a regular hexagon inscribed in a circle of unit radius. Then the product of the lengths of the line segments A₀ A₁ , A₀ A₂ , and A₀ A₄ is

(A) 3/4

(B) 3√3

(C) 3

(D) 3√3/2

Sol:

$\large (A_0 A_1)^2 = \frac{1}{4} + \frac{3}{4}= 1 $

A₀ A₁ = 1

A₀ A₂ = √3

A₀ A₄ = √3

Hence , ( A₀ A₁) (A₀ A₂ ) ( A₀ A₄ ) = 3

Hence (C) is the correct answer.