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AM = AN iff MN //KL (2004 Romania District VII P2)

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May 24, 2020
geometryangle bisectorequal segmentsparallel

Problem Statement

Let ABCABC be a triangle and DD a point on the side BCBC. The angle bisectors of ∠ADB,∠ADC\angle ADB ,\angle ADC intersect AB,ACAB ,AC at points M,NM ,N respectively. The angle bisectors of ∠ABD,∠ACD\angle ABD , \angle ACD intersects DM,DNDM , DN at points K,LK , L respectively. Prove that AM=ANAM = AN if and only if MNMN and KLKL are parallel.
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