Let be a triangle with and let be the midpoint of . The angle bisector of intersects the circle through and at the point inside the triangle . The line intersects the circle through and in two points and . The lines and meet at a point , and the lines and meet at a point . Show that is the incentre of triangle .

Proposed by Jan Vonk, Belgium and Hojoo Lee, South Korea

Proposed by Jan Vonk, Belgium and Hojoo Lee, South Korea