MathDB

P is a point moving on Ω.

Source: KöMaL, May 2020

March 12, 2021

geometryTangentscirclesincenterconcurrentreflection

Problem Statement

Two circles are given in the plane,

\Omega

and inside it

\omega

. The center of

\omega

is

I

.

P

is a point moving on

\Omega

. The second intersection of the tangents from

P

to

\omega

and circle

\Omega

are

Q

and

R.

The second intersection of circle

IQR

and lines

PI

,

PQ

and

PR

are

J

,

S

and

T,

respectively. The reflection of point

J

across line

ST

is

K.

Prove that lines

PK

are concurrent.

Back to Problems View on AoPS