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angle chasing, isosceles, equilateral (2009 Romania District VII P4)

Source:

May 19, 2020
anglesgeometryisoscelesEquilateral

Problem Statement

Let ABCABC be an equilateral ABCABC. Points M,N,PM, N, P are located on the sides AC,AB,BCAC, AB, BC, respectively, such that ∠CBM=12∠AMN=13∠BNP\angle CBM= \frac{1}{2} \angle AMN = \frac{1}{3} \angle BNP and ∠CMP=90o\angle CMP = 90 ^o. a) Show that △NMB\vartriangle NMB is isosceles. b) Determine ∠CBM\angle CBM.
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