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Angle bisector parallelism condition

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December 13, 2019
Gemetryangle bisectorgeometry

Problem Statement

Let M,N M,N be points on the segments AB,AC, AB,AC, respectively, of the triangle ABC. ABC. Also, let P,Q, P,Q, be the midpoints of the segments MN,BC, MN,BC, respectively. Knowing that PQ PQ is parallel to the bisector of ∠BAC, \angle BAC , show that BM=CN. BM=CN.
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