MathDB

2019 JBMO TST- North Macedonia, problem 2

Source: 2019 JBMO TST- North Macedonia

May 26, 2019

JMMOMacedoniaJunior2019geometrycircumcircle

Problem Statement

Circles

\omega_{1}

and

\omega_{2}

intersect at points

A

and

B

. Let

t_{1}

and

t_{2}

be the tangents to

\omega_{1}

and

\omega_{2}

, respectively, at point

A

. Let the second intersection of

\omega_{1}

and

t_{2}

be

C

, and let the second intersection of

\omega_{2}

and

t_{1}

be

D

. Points

P

and

E

lie on the ray

AB

, such that

B

lies between

A

and

P

,

P

lies between

A

and

E

, and

AE = 2 \cdot AP

. The circumcircle to

\bigtriangleup BCE

intersects

t_{2}

again at point

Q

, whereas the circumcircle to

\bigtriangleup BDE

intersects

t_{1}

again at point

R

. Prove that points

P

,

Q

, and

R

are collinear.

Back to Problems View on AoPS