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6 geometry problems out of 8 at our TST so far..

Source: Moldova 2007 IMO-BMO TST II problem 3

March 23, 2007

geometryratiotrigonometrycircumcircletrapezoidradical axisprojective geometry

Problem Statement

Let

M, N

be points inside the angle

\angle BAC

usch that

\angle MAB\equiv \angle NAC

. If

M_{1}, M_{2}

and

N_{1}, N_{2}

are the projections of

M

and

N

AB, AC

respectively then prove that

M, N

and

P

the intersection of

M_{1}N_{2}

with

N_{1}M_{2}

are collinear.