MathDB

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

Source: Sharygin 2006 IX- X CR 11

August 23, 2019

concurrencyconcurrentCircumcentergeometrycircumcircle

Problem Statement

In the triangle

ABC, O

is the center of the circumscribed circle,

A ', B', C '

are the symmetrics of

A, B, C

with respect to opposite sides,

A_1, B_1, C_1

are the intersection points of the lines

OA'

and

BC, OB'

and

AC, OC'

and

AB

. Prove that the lines

A A_1, BB_1, CC_1

intersect at one point.