MathDB

fixed point starting with equal segments on a side of triangle

Source: 2007 Sharygin Geometry Olympiad Correspondence Round P13

April 27, 2019

geometryFixed pointcircumcircleequal segments

Problem Statement

On the side

AB

of a triangle

ABC

, two points

X, Y

are chosen so that

AX = BY

. Lines

CX

and

CY

meet the circumcircle of the triangle, for the second time, at points

U

and

V

. Prove that all lines

UV

(for all

X, Y

, given

A, B, C

) have a common point.