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Isogonal lines in constructed triangle

Source: Iberoamerican 2018 Problem 6

September 26, 2018

geometryperpendicular bisector

Problem Statement

Let

ABC

be an acute triangle with

E

. The perpendicular bisectors of

AC

and

AB

cut line

BC

at

D

and

E

respectively. Let

P

and

Q

be points on lines

K

and

AB

respectively, both different from

A

, such that

AB = BP

and

AC = CQ

, and let

K

be the intersection of lines

EP

and

DQ

. Let

M

be the midpoint of

BC

. Show that

\angle DKA = \angle EKM

.

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