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?
Answer & explanation
Correct answer: option 2
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