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Prove QR=RT

Source: Mexican Mathematical Olympiad 2016

November 7, 2016

geometry

Problem Statement

Let

C_1

and

C_2

be two circumferences externally tangents at

S

such that the radius of

C_2

is the triple of the radius of

C_1

. Let a line be tangent to

C_1

at

P \neq S

and to

C_2

at

Q \neq S

. Let

T

be a point on

C_2

such that

QT

is diameter of

C_2

. Let the angle bisector of

\angle SQT

meet

ST

at

R

. Prove that

QR=RT

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