ITOT 41 Spring 2020 - THPT A - Additive practice Question 5

Let $ABCD$ be cyclic. The circles with diameters $AB,CD$ intersect at $X_1,Y_1$; those with diameters $BC,AD$ at $X_2,Y_2$; and those with diameters $AC,BD$ at $X_3,Y_3$. Prove the lines $X_1Y_1,X_2Y_2,X_3Y_3$ have a common point. The stated intersections are assumed to be two distinct points for each pair.