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Tangency and circles

Source: Poland 2014 - Second Round P5

July 28, 2019
geometrycircles

Problem Statement

Circles o1o_1 and o2o_2 tangent to some line at points AA and BB, respectively, intersect at points XX and YY (XX is closer to the line ABAB). Line AXAX intersects o2o_2 at point P≠XP\neq X. Tangent to o2o_2 at point PP intersects line ABAB at point QQ. Prove that ∢XYB=∢BYQ\sphericalangle XYB = \sphericalangle BYQ.
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