MathDB

2

Part of 1993 Poland - Second Round

Problems(1)

fixed concurrency point as line passing through a point varies

Source: Polish second round 1993 p2

1/19/2020
Let be given a circle with center OO and a point PP outside the circle. A line ll passes through PP and cuts the circle at AA and BB. Let CC be the point symmetric to AA with respect to OPOP, and let mm be the line BCBC. Prove that all lines mm have a common point as ll varies.
geometryfixedconcurrencyconcurrentFixed point