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2013 HMIC p3 geometry

Source:

September 20, 2019

circumcirclegeometry

Problem Statement

Triangle

ABC

is inscribed in a circle

\omega

such that

\angle A = 60^o

and

\angle B = 75^o

. Let the bisector of angle

A

meet

BC

and

\omega

at

E

and

D

, respectively. Let the reflections of

A

across

D

and

C

be

D'

and

C'

, respectively. If the tangent to

\omega

at

A

meets line

BC

at

P

, and the circumcircle of

APD'

meets line

AC

at

F \ne A

, prove that the circumcircle of

C'FE

is tangent to

BC

at

E

.

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