Let ABCD be a trapezoid with bases BC∥AD, where AD>BC, and non-parallel legs AB and CD. Let M be the intersection of AC and BD. Let Γ1 be a circumference that passes through M and is tangent to AD at point A; let Γ2 be a circumference that passes through M and is tangent to AD at point D. Let S be the intersection of the lines AB and CD, X the intersection of Γ1 with the line AS, Y the intesection of Γ2 with the line DS, and O the circumcenter of triangle ASD.
Show that SO⊥XY. geometrytrapezoidcircumcircleArgentinaTST