In the given figure, E and F are the centers of two identical circles. What is the ratio of area of triangle AOB to the area of triangle DOC?

1 : 9

Here in ∆AEB and ∆XED,

AE = XE = radius, ∠EAB = ∠EXD = 90 and ∠EBA = ∠EDX (AB and DC are parallel)

⇒ ∆AEB and ∆XED will be similar and in the same way ∆BFA and ∆YFC will also be similar

⇒ DX = AB = YC

⇒ AB ∶ DC = 1 ∶ 3

Since ratio of areas of 2 triangles is equal to the ratio of square of their sides

∴ Area ∆AOB ∶ Area ∆DOC = 1 ∶ 9