6

Part of 2012 Swedish Mathematical Competition

Problems(1)

intersection of diagonals in a tangential trapezoid lies on a diameter _|_ bases

Source: 2012 (-13) Swedish Mathematical Competition p6

A circle is inscribed in an trapezoid. Show that the diagonals of the trapezoid intersect at a point on the diameter of the circle perpendicular to the two parallel sides.

geometrytrapezoiddiametertangential