MathDB

10.6

Part of 2001 All-Russian Olympiad Regional Round

Problems(1)

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

Source:

9/26/2024
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.
geometryparallelogramtangent