MathDB

The triangle

ABC

is given. On the arc

BC

of its circumscribed circle, which does not contain point

A

, the variable point

X

is selected, and on the rays

XB

and

XC

, the variable points

Y

and

Z

, respectively, so that

XA = XY = XZ

. Prove that the line

YZ

passes through a fixed point. Proposed by A. Kuznetsov

Problem Statement