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Show that ∠AKM = ∠KPC - [UKRMO 2009 Grade 8]

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January 21, 2011
geometryangle bisector

Problem Statement

In the triangle ABCABC given that ∠ABC=120∘.\angle ABC = 120^\circ . The bisector of ∠B\angle B meet ACAC at MM and external bisector of ∠BCA\angle BCA meet ABAB at P.P. Segments MPMP and BCBC intersects at KK. Prove that ∠AKM=∠KPC.\angle AKM = \angle KPC .
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