Question

A rhombus MNOP is drawn inside a circle ( whose center is O )such that vertices M,N and P of the rhombus lie on the boundary of the circle. If the area of the rhombus is 96√3cm² , find the area of the circle
Hint:_ _ _πcm² ( three numbers should be filled)

Answer 1

Answer:

192

Step-by-step explanation:

Since OM= OP = ON

the rhombus can be divided into two equilateral triangles whose side is equal to the radius of the circle

Let the radius of the circle be x.

Since area of a equilateral triangle with side x is (√3*x^2) /4, with two such triangles forming rhombus makes area equal to (√3*x^2) /2.

Since (√3*x^2) /2 = 96√3

x^2= 192

Since area of the circle is πx^2

= 192π cm^2