Question

ABCD is a square inscribed in a circle of radius 14 cm. E, F, G and H are the midpoints of the sides DA, AB, BC and CD respectively. The area of the square EFGH will be

(a) 89 cm² 

(b) 196 cm²  

(c) 98 cm² 

(d) 392 cm² 

Answer 1

(b) 196 cm²

Given, OA = 14 cm ⇒ AC = 28 cm 

Let AB = BC = a ⇒ a² + a² = 28²

⇒ 2a² = 28 x 28 ⇒ a² = \(\frac{28\times28}{2}\) = 392

⇒ Area of square ABCD = 392 cm²

Area of square EFGH = \(\frac12\) x 392 cm² = 196 cm²