MathDB

2007 JBMO Shortlist G4

Source: 2007 JBMO Shortlist G4

October 10, 2017

JBMOgeometry

Problem Statement

Let

S

be a point inside

\angle pOq

, and let

k

be a circle which contains

S

and touches the legs

Op

and

Oq

in points

P

and

Q

respectively. Straight line

s

parallel to

Op

from

S

intersects

Oq

in a point

R

. Let

T

be the intersection point of the ray

PS

and circumscribed circle of

\vartriangle SQR

and

T \ne S

. Prove that

OT // SQ

and

OT

is a tangent of the circumscribed circle of

\vartriangle SQR

.

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