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Distance between the circumcenters of triangles

Source: Sharygin Geometry Olympiad Correspondence round 2016 P-6 Grade-8

February 20, 2017

geometrycircumcircle

Problem Statement

Let

M

be the midpoint of side

AC

of triangle

ABC

MD

and

ME

be the perpendiculars from

M

AB

and

BC

respectively. Prove that the distance between the circumcenters of triangles

ABE

and

BCD

is equal to

AC/4

(Proposed by M.Volchkevich)