MathDB

AIMO 5/1, German TST 2010

Source: AIMO 5/1, German TST 2010

July 16, 2011

geometry unsolvedgeometry

Problem Statement

In the plane we have points

P,Q,A,B,C

such triangles

APQ,QBP

and

PQC

are similar accordantly (same direction). Then let

A'

(

B',C'

respectively) be the intersection of lines

BP

and

CQ

(

CP

and

AQ;

AP

and

BQ,

respectively.) Show that the points

A,B,C,A',B',C'

lie on a circle.