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Angle equality

Source: Sharygin Geometry Olympiad Correspondence round 2016 P-5 Grade-8

February 20, 2017

geometry

Problem Statement

In quadrilateral

ABCD

AB = CD

M

and

K

are the midpoints of

BC

and

AD

.Prove that the angle between

MK

and

AC

is equal to the half-sum of angles

BAC

and

DCA

(Proposed by M.Volchkevich)