Question

ABCD, EFGH, and HIJK are squares.

AABCD = 400 cm2, O is the center of the circle, O ∈
FE
,
FG
and
BC
tangent to the circle (see the picture on the right).

Find the area of the square HIJK.

Answer 1

400/81 cm²

Explanation:

FE : DC

1 : 3

Since area ABCD = 400

s² = 400

s = 20

FE = ⅓(20) = 20/3 cm

IH : FE

1 : 3

IH = ⅓(20/3) = 20/9 cm

Area of HIJK:

(20/9)² = 400/81 cm²