MathDB

11

Part of 2006 Sharygin Geometry Olympiad

Problems(1)

concurrency related to symmetric of A,B,C wrt opposite sides, circumcenter

Source: Sharygin 2006 IX- X CR 11

8/23/2019
In the triangle ABC,OABC, O is the center of the circumscribed circle, A′,B′,C′A ', B', C ' are the symmetrics of A,B,CA, B, C with respect to opposite sides, A1,B1,C1 A_1, B_1, C_1 are the intersection points of the lines OA′OA' and BC,OB′BC, OB' and AC,OC′AC, OC' and ABAB. Prove that the lines AA1,BB1,CC1A A_1, BB_1, CC_1 intersect at one point.
concurrencyconcurrentCircumcentergeometrycircumcircle