Find the ratio of the areas of the in-circle and circum-circle of an equilateral triangle?

Please give the answer in details.

1 Answer
Nov 5, 2016

1:4

Explanation:

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Given Delta ABC = equilateral triangle
Let radius of in-circle be r, and radius of circumcircle be R.
In Delta OBD, angleOBD=30^@, angle ODB=90^@ => R=2r

Let area of in-circle be A_I and area of circumcircle be A_C,

=> A_I/A_C=(pir^2)/(pi(R^2))=(pir^2)/(pi(2r)^2)=1/4

Hence, A_I : A_C = 1:4