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AC _|_ OQ wanted, 2 circles, tangent related

Source: 2006 VMEO III Seniors 12.1 Vietnamese Mathematics e - Olympiad https://artofproblemsolving.com/community/c2463155_vmeo_iii

September 17, 2021
perpendiculargeometry

Problem Statement

Given a circle (O)(O) and a point PP outside that circle. MM is a point running on the circle (O)(O). The circle with center II and diameter PMPM intersects circle (O)(O) again at NN. The tangent of (I)(I) at PP intersects MNMN at QQ. The line through QQ perpendicular to POPO intersects PMPM at A A. ANAN intersects (O)(O) further at B B. BMBM intersects POPO at CC. Prove that ACAC is perpendicular to OQOQ.
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