MathDB

P5

Part of 2014 Iranian Geometry Olympiad (junior)

Problems(1)

inequality with midpoint of arc with equal angles

Source: IGO 2014 Junior 5

7/22/2018
Two points X,YX, Y lie on the arc BCBC of the circumcircle of △ABC\triangle ABC (this arc does not contain AA) such that ∠BAX=∠CAY\angle BAX = \angle CAY . Let MM denotes the midpoint of the chord AXAX . Show that BM+CM>AYBM +CM > AY .
by Mahan Tajrobekar
geometrycircumcirclearc midpointgeometric inequality