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Geometry in XMO, don't discuss until tomorrow

Source: 11th XMO Test 2 P1

February 13, 2023
geometryxmo

Problem Statement

Let △ABC\triangle ABC be connected to the circle Γ\Gamma. The angular bisector of ∠BAC\angle BAC intersects BCBC to DD. Straight line BPBP intersects ACAC to EE, and straight line CPCP intersects ABAB to FF. Let the tangent of the circle Γ\Gamma at point AA intersect the line EFEF at the point QQ. Proof: PQ∥BCPQ\parallel BC.
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