MathDB

Paraguayan National Olympiad 2010, Level 3, Problem 5

Source:

September 23, 2014

geometrycircumcircle

Problem Statement

In a triangle

ABC

, let

D

E

and

F

be the feet of the altitudes from

A

B

and

C

respectively. Let

D'

E'

and

F'

be the second intersection of lines

AD

BE

and

CF

with the circumcircle of

ABC

. Show that the triangles

DEF

and

D'E'F'

are similar.