MathDB
Two Tangent Circles

Source: Simurgh 2019 - Problem 2

February 24, 2019
circumcirclegeometry

Problem Statement

Let ABCABC be a triangle with AB=ACAB=AC. Let point QQ be on plane such that AQ∥BCAQ \parallel BC and AQ=ABAQ = AB. Now let the PP be the foot of perpendicular from QQ to BCBC. Show that the circle with diameter PQPQ is tangent to the circumcircle of triangle ABCABC.
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