MathDB

Let

\triangle ABC

and

\triangle C'B'A

be two congruent triangles ( with this order and orient. ). Define point

M

as the midpoint of segment

AB

and suppose that the extension of

CB'

from

B'

passes trough

M

, if

F

be a point on the smaller arc

MC

of circumcircle of triangle

\triangle BMC

such that

\angle FB'A=90

and

\angle C'CB' \neq 90

, then prove that

\angle B'C'C=\angle CAF

.
Proposed by Alireza Dadgarnia

Problem Statement