MathDB

13

Part of 2014 Sharygin Geometry Olympiad

Problems(1)

prove that the circumcenter of a triangle moves along a straight line

Source: Sharygin Geometry Olympiad 2014 Correspondence Round P13

8/1/2018
Let ACAC be a fixed chord of a circle ω\omega with center OO. Point BB moves along the arc ACAC. A fixed point PP lies on ACAC. The line passing through PP and parallel to AOAO meets BABA at point A1A_1, the line passing through PP and parallel to COCO meets BCBC at point C1C_1. Prove that the circumcenter of triangle A1BC1A_1BC_1 moves along a straight line.
geometryLocusCircumcenter