10 coins arounc a circle
Source: VII May Olympiad (Olimpiada de Mayo) 2001 L2 P4
September 19, 2022
geometryareas
Problem Statement
Ten coins of cm radius are placed around a circle as indicated in the figure.
Each coin is tangent to the circle and its two neighboring coins.
Prove that the sum of the areas of the ten coins is twice the area of the circle.
https://cdn.artofproblemsolving.com/attachments/5/e/edf7a7d39d749748f4ae818853cb3f8b2b35b5.gif