Circles in rhombus
Source: 44th International Tournament of Towns, Senior O-Level P2, Fall 2022
February 16, 2023
geometryTournament of Towns
Problem Statement
A big circle is inscribed in a rhombus, each of two smaller circles touches two sides of the rhombus and the big circle as shown in the figure on the right. Prove that the four dashed lines spanning the points where the circles touch the rhombus as shown in the figure make up a square.