MathDB

2002.2

Part of Champions Tournament Seniors - geometry

Problems(1)

perpendicular wanted, tangent and secant to a circle related

Source: Champions Tournament (Ukraine) - Турнір чемпіонів - 2002 Seniors p2

9/6/2020
The point PP is outside the circle ω\omega with center OO. Lines ℓ1\ell_1 and ℓ2\ell_2 pass through a point PP, ℓ1\ell_1 touches the circle ω\omega at the point AA and ℓ2\ell_2 intersects ω\omega at the points BB and CC. Tangent to the circle ω\omega at points BB and CC intersect at point QQ. Let KK be the point of intersection of the lines BCBC and AQAQ. Prove that (OK)⊥(PQ)(OK) \perp (PQ).
geometryperpendiculartangentsecantChampions Tournament