MathDB

Depressed geometry

Source: 2023 Serbia TST Problem 2

May 22, 2023

geometrySerbiaTSTcircumcircle

Problem Statement

A circle centered at

A

intersects sides

AC

and

AB

of

\triangle ABC

at

E

and

F

, and the circumcircle of

\triangle ABC

at

X

and

Y

. Let

D

be the point on

BC

such that

AD

,

BE

,

CF

concur. Let

P=XE\cap YF

and

Q=XF\cap YE

. Prove that the foot of the perpendicular from

D

to

EF

lies on

PQ

.

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