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A, E and F are collinear

Source: Iberoamerican Olympiad 2016-P5

September 28, 2016

geometry

Problem Statement

The circumferences

C_1

and

C_2

cut each other at different points

A

and

K

. The common tangent to

C_1

and

C_2

nearer to

K

touches

C_1

at

B

and

C_2

at

C

. Let

P

be the foot of the perpendicular from

B

to

AC

, and let

Q

be the foot of the perpendicular from

C

to

AB

. If

E

and

F

are the symmetric points of

K

with respect to the lines

PQ

and

BC

, respectively, prove that

A, E

and

F

are collinear.

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