SHARYGIN 2012 Problem 18

A triangle and two points inside it are marked. It is known that one of the triangle's angles is equal to $58^{\circ}$ , one of two remaining angles is equal to $59^{\circ}$ , one of two given points is the incenter of the triangle and the second one is its circumcenter. Using only the ruler without partitions determine where is each of the angles and where is each of the centers.