MathDB

Around triangle

ABC

with acute angle C is circumscribed a circle. On the arc

AB

, which does not contain point

C

, point

D

is chosen. Point

D'

is symmetric on point

D

with respect to line

AB

. Straight lines

AD'

and

BD'

intersect segments

BC

and

AC

at points

E

and

F

. Let point

C

move along its arc

AB

. Prove that the center of the circumscribed circle of a triangle

CEF

moves on a straight line.

Problem Statement