Question

Show that the area of the circumcircle of a square is twice the area the incircle of the same square.

Answer 1

We know a square of side ‘a’ has its diagonal a√2.

For inscribed circle of such square (with side as a), the circle diameter is 'a' and diameter of the superscribed circle is a√2.

So, area of the inscribed circle is 1/4 * πa^2 and area of the superscribed circle is 1/4 “ 2πa^2 or 1/2 * πa^2

This is reason why for a square , area of superscribed circle is twice the area of its inscribed circle.

For example, for square of side 2cm, area of it's inscribed and circumscribed circle are 1/4 * π* 2^2 or π and 1/4 * π * (2√2)^2 or 2π which is double of area of inscribed circle.