MathDB

Concyclicity Implies Perpendicularity

Source: Turkey EGMO TST 2014 P1

August 6, 2016

geometrycircumcircle

Problem Statement

Let

D

be the midpoint of the side

BC

of a triangle

ABC

and

AD

intersect the circumcircle of

ABC

for the second time at

E

. Let

P

be the point symmetric to the point

E

with respect to the point

D

and

Q

be the point of intersection of the lines

CP

and

AB

. Prove that if

A,C,D,Q

are concyclic, then the lines

BP

and

AC

are perpendicular.

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