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Tuymaada 2017 Seniors Q7

Source: Tuymaada 2017 Seniors Q7 (day 2 P3)

September 26, 2017

tangentrectanglegeometry

Problem Statement

A point

E

lies on the extension of the side

AD

of the rectangle

ABCD

over

D

. The ray

EC

meets the circumcircle

\omega

of

ABE

at the point

\ell

. The rays

DC

and

AF

meet at

P

.

H

is the foot of the perpendicular drawn from

C

to the line

\ell

going through

E

and parallel to

AF

. Prove that the line

PH

is tangent to

\omega

.
(A. Kuznetsov)

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