MathDB

PAMO Problem 4: Perpendicular lines

Source: 2019 Pan-African Mathematics Olympiad, Problem 4

April 9, 2019

geometryPAMOcircumcircle

Problem Statement

The tangents to the circumcircle of

\triangle ABC

B

and

C

meet at

D

. The circumcircle of

\triangle BCD

meets sides

AC

and

AB

again at

E

and

F

respectively. Let

O

be the circumcentre of

\triangle ABC

. Show that

AO

is perpendicular to

EF