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Isosceles triangle

Source: Romanian TST 2002

March 19, 2004

ratiogeometryrectanglegeometry proposed

Problem Statement

Let

M

and

N

be the midpoints of the respective sides

AB

and

AC

of an acute-angled triangle

ABC

. Let

P

be the foot of the perpendicular from

N

onto

BC

and let

A_1

be the midpoint of

MP

. Points

B_1

and

C_1

are obtained similarly. If

AA_1

,

BB_1

and

CC_1

are concurrent, show that the triangle

ABC

is isosceles.
Mircea Becheanu

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