MathDB

lines concurrent with circumcircle

Source: Balkan BMO Shortlist 2015 G7

August 6, 2019

concurrencyconcurrentorthocentercircumcirclegeometry

Problem Statement

Let scalene triangle

ABC

have orthocentre

H

and circumcircle

\Gamma

.

AH

meets

\Gamma

at

D

distinct from

A

.

BH

and

CH

meet

CA

and

AB

at

E

and

F

respectively, and

EF

meets

BC

at

P

. The tangents to

\Gamma

at

B

and

C

meet at

T

. Show that

AP

and

DT

are concurrent on the circumcircle of

AFE

.

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