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Prove M P · OA = BC · OQ

Source: IberoAmerican 1989 Q4

November 27, 2010

geometryincentergeometry proposed

Problem Statement

The incircle of the triangle

ABC

is tangent to sides

AC

and

BC

at

M

and

N

, respectively. The bisectors of the angles at

A

and

B

intersect

MN

at points

P

and

Q

, respectively. Let

O

be the incentre of

\triangle ABC

. Prove that

MP\cdot OA=BC\cdot OQ

.

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