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Serbian Junior TST

Source: Serbia Junior TST 2016 P1

May 21, 2016

geometry

Problem Statement

Let rightangled

\triangle ABC

be given with right angle at vertex

C

. Let

D

be foot of altitude from

C

and let

k

be circle that touches

BD

at

E

,

CD

at

F

and circumcircle of

\triangle ABC

at

G

.

a.)

Prove that points

A

,

F

and

G

are collinear.

b.)

Express radius of circle

k

in terms of sides of

\triangle ABC

.

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