Problem

Source: Israel Autumn 2016 TST2/1

Tags: geometry, trapezoid



A square ABCD is given. A point P is chosen inside the triangle ABC such that CAP=15=BCP. A point Q is chosen such that APCQ is an isosceles trapezoid: PCAQ, and AP=CQ,AP. Denote by N the midpoint of PQ. Find the angles of the triangle CAN.