9

Part of 2006 JBMO ShortLists

Problems(1)

Trapezoid and lengths

Source: JBMO Shortlist 2006

ABCD

be a trapezoid with

AB\parallel CD,AB>CD

and \angle{A} \plus{} \angle{B} \equal{} 90^\circ. Prove that the distance between the midpoints of the bases is equal to the semidifference of the bases.

geometrytrapezoidgeometry proposed