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trig relation with two equal circles, each passing through center of other

Source: Sharygin 2010 Final 10.2

November 25, 2018
geometrytrigonometrycirclescircumcircletrigonometric

Problem Statement

Each of two equal circles ω1\omega_1 and ω2\omega_2 passes through the center of the other one. Triangle ABCABC is inscribed into ω1\omega_1, and lines AC,BCAC, BC touch ω2\omega_2 . Prove that cosA+cosB=1cosA + cosB = 1.
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