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Externally Tangent Circles in an Angle Part I

Source: Sharygin Geometry Olympiad 2014 - Problem 9

November 15, 2014
geometry unsolvedgeometry

Problem Statement

Two circles ω1\omega_1 and ω2\omega_2 touching externally at point LL are inscribed into angle BACBAC. Circle ω1\omega_1 touches ray ABAB at point EE, and circle ω2\omega_2 touches ray ACAC at point MM. Line ELEL meets ω2\omega_2 for the second time at point QQ. Prove that MQ∥ALMQ\parallel AL.
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