MathDB

IZhO 2024, P2

Source:

January 9, 2024

geometry

Problem Statement

Circles

\Omega

and

\Gamma

meet at points

A

and

B

. The line containing their centres intersects

\Omega

and

\Gamma

at point

P

and

Q

, respectively, such that these points lie on same side of the line

AB

and point

Q

is closer to

AB

than point

P

. The circle

\delta

lies on the same side of the line

AB

as

P

and

Q

, touches the segment

AB

at point

D

and touches

\Gamma

at point

T

. The line

PD

meets

\delta

and

\Omega

again at points

K

and

L

, respectively. Prove that

\angle QTK=\angle DTL

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