Question

In fig. , OPQR is a rhombus whose three vertices P, Q, R lie on a circle of radius 8 cm.Find the area of the shaded region.

Answer 1

see diagram.

O is center of the circle. a = 8 cm (given)
b = OQ = a  ;;       d = PR = ?

In a Rhombus, 4 a² = b² + d²    (diagonals)
      So  d = √3 a = 8 √3  cm

Area = bd/2 = 8*8√3 /2 = 32 √3 cm