The incircle of a cyclic quadrilateral ABCD tangents the four sides at E, F, G, H in counterclockwise order. Let I be the incenter and O be the circumcenter of ABCD. Show that the line connecting the centers of ⊙(OEG) and ⊙(OFH) is perpendicular to OI. geometryradical axistangential quadrilateralperpendicular