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IMOC 2020 G6 2 tangents of different circle concurrent with a line

Source: https://artofproblemsolving.com/community/c6h2254883p17398793

September 1, 2020
geometryconcurrencyTangentsmidpoint

Problem Statement

Let ABCABC be a triangle, and Ma,Mb,McM_a, M_b, M_c be the midpoints of BC,CA,ABBC, CA, AB, respectively. Extend MbMcM_bM_c so that it intersects ⊙(ABC)\odot (ABC) at PP. Let APAP and BCBC intersect at QQ. Prove that the tangent at AA to ⊙(ABC)\odot(ABC) and the tangent at PP to ⊙(PQMa)\odot (P QM_a) intersect on line BCBC.
(Li4)
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