A circle centred at I is tangent to the sides BC,CA, and AB of an acute-angled triangle ABC at A1,B1, and C1, respectively. Let K and L be the incenters of the quadrilaterals AB1IC1 and BA1IC1, respectively. Let CH be an altitude of triangle ABC. Let the internal angle bisectors of angles AHC and BHC meet the lines A1C1 and B1C1 at P and Q, respectively. Prove that Q is the orthocenter of the triangle KLP.Kolmogorov Cup 2018, Major League, Day 3, Problem 1; A. Zaslavsky geometryorthocentercircleIncentersangle bisectorKvant