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Incircle, and a tangency of circle and a line

Source: Iran TST 2007, Day 2

May 7, 2007

geometryincentergeometric transformationhomothetytrapezoidanalytic geometryreflection

Problem Statement

Let

\omega

be incircle of

ABC

.

P

and

\omega

are on

F,E

and

AC

, such that

PQ

is parallel to

BC

and is tangent to

\omega

.

AB,AC

touch

\omega

at

F,E

. Prove that if

M

is midpoint of

PQ

, and

T

is intersection point of

EF

and

BC

, then

TM

is tangent to

\omega

. By Ali Khezeli

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