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Intersection of tangents to circles passing through two vertices of a triangle

Source: 2018 Pan-African Shortlist - G2

May 7, 2019
geometryTangentsTriangle

Problem Statement

Let PP be a point on the median AMAM of a triangle ABCABC. Suppose that the tangents to the circumcircles of ABPABP and ACPACP at BB and CC respectively meet at QQ. Show that ∠PAB=∠CAQ\angle PAB = \angle CAQ.
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