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Lines meet on perpendicular bisector

Source: Mexico National Olympiad Mock Exam 2021 P4

November 12, 2021

geometryperpendicular bisector

Problem Statement

Let

C

be an obtuse triangle with

AB = AC

, and let

\Gamma

be the circle that is tangent to

AB

at

B

and to

AC

at

C

. Let

D

be the point on

\Gamma

furthest from

A

such that

AD

is perpendicular to

BC

. Point

E

is the intersection of

AB

and

DC

, and point

F

lies on line

AB

such that

BC = BF

and

B

lies on segment

AF

. Finally, let

P

be the intersection of lines

AC

and

DB

. Show that

PE = PF

.

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