MathDB

2013 HMMT Geometry # 10

Source:

March 3, 2024

geometry

Problem Statement

Triangle

ABC

is inscribed in a circle

\omega

. Let the bisector of angle

A

meet

\omega

at

D

and

BC

at

E

. Let the reflections of

A

across

D

and

C

be

D'

and

C'

, respectively. Suppose that

A

,

AB = 3

, and

P

. If the tangent to

\omega

at

A

meets line

BC

at

P

, and the circumcircle of APD' meets line

BC

at

F

(other than

P

), compute

FC'

.

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