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If two circles are tangent, then all three are

Source: Tuymaada 2014, Day 2, Problem 2, Junior League

July 12, 2014
trigonometrygeometry unsolvedgeometryTuymaada

Problem Statement

Radius of the circle ωA\omega_A with centre at vertex AA of a triangle △ABC\triangle{ABC} is equal to the radius of the excircle tangent to BCBC. The circles ωB\omega_B and ωC\omega_C are defined similarly. Prove that if two of these circles are tangent then every two of them are tangent to each other.
(L. Emelyanov)
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