View source for 2018 OIM Problems/Problem 6

== Problem ==
Let <math>ABC</math> be an acute triangle with <math>AC > AB > BC</math>. The perpendicular bisectors of <math>AC</math> and <math>AB</math> cut the line <math>BC</math> at <math>D</math> and <math>E</math>, respectively. Let <math>P</math> and <math>Q</math> be points other than <math>A</math> on the lines <math>AC</math> and <math>AB</math>, respectively, such that <math>AB = BP</math> and <math>AC = CQ</math>, and let <math>K</math> be the intersection of the lines <math>EP</math> and <math>DQ</math>. Let <math>M</math> be the midpoint of <math>BC</math>. Show that <math>\angle DKA = \angle EKM</math>.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

== Solution ==
{{solution}}

== See also ==
[[OIM Problems and Solutions]]