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 A_{0} A_{1} , A_{0} A_{2} , and A_{0} A_{4} 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 $

A_{0} A_{1} = 1

A_{0} A_{2} = √3

A_{0} A_{4} = √3

Hence , ( A_{0} A_{1}) (A_{0} A_{2} ) ( A_{0} A_{4} ) = 3

Hence (C) is the correct answer.