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Tangents to circle concurrent on a line

Source: Romania TST 3 2012, Problem 2

May 11, 2012

projective geometrygeometry proposedgeometry

Problem Statement

Let

\gamma

be a circle and

l

a line in its plane. Let

K

be a point on

l

, located outside of

\gamma

. Let

KA

and

KB

be the tangents from

K

to

\gamma

, where

l

and

R

are distinct points on

S

. Let

QR

and

Q

be two points on

\gamma

. Lines

PA

and

D

intersect line

l

in two points

R

and respectively

S

. Lines

QR

and

QS

intersect the second time circle

\gamma

in points

C

and

D

. Prove that the tangents from

C

and

D

to

\gamma

are concurrent on line

l

.

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