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tangent at Q is // to AC - All-Russian MO 2001 Regional (R4) 10.6

Source:

September 26, 2024
geometryparallelogramtangent

Problem Statement

Given triangle ABCABC. Point B1B_1 is marked on line ACAC so that AB=AB1AB = AB_1, while B1B_1 and CC are on the same side of AA. Through points CC, B1B_1 and the foot of the bisector of angle AA of triangle ABCABC, a circle ω\omega is drawn, intersecting for second time the circle circumscribed around triangle ABCABC, at point QQ. Prove that the tangent drawn to ω\omega at point QQ is parallel to ACAC.
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