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midpoint of segment circumcentres equidistant from 2 points

Source: Tuymaada 2019 p2

July 22, 2019

geometrytrapezoidCircumcentermidpointdistance

Problem Statement

A trapezoid

ABCD

with

BC // AD

is given. The points

B'

and

C'

are symmetrical to

B

and

C

with respect to

CD

and

AB

, respectively. Prove that the midpoint of the segment joining the circumcentres of

ABC'

and

B'CD

is equidistant from

A

and

D