Inscribed and Circumscribed Circles
Geometry
Level
2
\(ABCD\) is a square. \(\Gamma_1\) is a circle that circumscribes \(ABCD\) (i.e. \(\Gamma_1\) passes through points \(A, B, C\) and \(D\)). \(\Gamma_2\) is a circle that is inscribed in \(ABCD\) (i.e. \(\Gamma_2\) is tangential to sides \(AB, BC, CD\) and \(DA\)). If the area of \(\Gamma_1\) is \( 100\), what is the area of \(\Gamma_2\)?
by
Calvin Lin