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Costa Rican Math Olympiad Problem 6 2009

Source:

November 29, 2009

geometrygeometry solvedprojective geometryPolarsPascal s theorem

Problem Statement

Let

\Delta ABC

with incircle

\Gamma

, let

D, E

and

a)

the tangency points of

\Gamma

with sides

BC, AC

and

AB

, respectively and let

P

the intersection point of

AD

with

\Gamma

.

a)

Prove that

BC, EF

and the straight line tangent to

\Gamma

for

P

concur at a point

A'

.

b)

Define

B'

and

C'

in an anologous way than

A'

. Prove that A'\minus{}B'\minus{}C'

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