MathDB

IMO Shortlist 2008, Geometry problem 4

Source: IMO Shortlist 2008, Geometry problem 4, German TST 5, P3, 2009

July 9, 2009

geometrycircumcirclereflectionIMO Shortlist

Problem Statement

In an acute triangle

ABC

segments

BE

and

CF

are altitudes. Two circles passing through the point

A

and

F

and tangent to the line

BC

at the points

P

and

Q

so that

B

lies between

C

and

Q

. Prove that lines

PE

and

QF

intersect on the circumcircle of triangle

AEF

.
Proposed by Davood Vakili, Iran