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Midline and tangent related geo, equal angles wanted

Source: IMOC 2021 G2

August 11, 2021
geometrycircumcircle

Problem Statement

Let the midline of △ABC\triangle ABC parallel to BCBC intersect the circumcircle Γ\Gamma of △ABC\triangle ABC at PP, QQ, and the tangent of Γ\Gamma at AA intersects BCBC at TT. Show that ∡BTQ=∡PTA\measuredangle BTQ = \measuredangle PTA.
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