5

Part of 2014 Czech and Slovak Olympiad III A

Problems(1)

3 circles given, collinearity wanted

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 2014 p5

Given is the acute triangle

ABC

. Let us denote

k

a circle with diameter

AB

. Another circle, tangent to

AB

A

and passing through point

C

intersects the circle

k

P, P \ne A

. Another circle which touches AB at point

B

and passes point

C

, intersects the circle

k

Q, Q \ne B

. Prove that the intersection of the line

AQ

BP

lies on one of the sides of angle

ACB

.
(Peter Novotný)

circlescollineargeometry