Question

Ratio of area of Incircle and Circumcircle of a triangle?

Answer 1

Given ΔABC= equilateral triangle
Let radius of in-circle be r, and radius of circumcircle be R.
In ΔOBD,∠OBD=30∘,∠ODB=90∘⇒R=2r

Let area of in-circle be AI and area of circumcircle be AC,

⇒AIAC=πr2π(R2)=πr2π(2r)2=14

Hence, AI:AC=1:4