Problem

Source: 2015 Saudi Arabia JBMO TST 1.3

Tags: geometry, circumcircle, right triangle, right angle



A right triangle ABC with C=90o is inscribed in a circle. Suppose that K is the midpoint of the arc BC that does not contain A. Let N be the midpoint of the segment AC, and M be the intersection point of the ray KN and the circle.The tangents to the circle drawn at A and C meet at E. prove that EMK=90o