The picture shows $10$ equal regular pentagons where each two neighbouring pentagons have a common side. The smaller circle is tangent to one side of each pentagon and the larger circle passes through the opposite vertices of these sides. Find the area of the larger circle if the area of the smaller circle is $1$.
Problem
Source: 2003 Estonia National Olympiad Final Round grade 10 p1
Tags: geometry, areas, Regular, pentagon, circles