MathDB

Trapezoid Midpoints

Source: AIME 2008II Problem 5

April 3, 2008

geometrytrapezoidratiocircumcircleanalytic geometrygeometric transformationhomothety

Problem Statement

In trapezoid

ABCD

with

\overline{BC}\parallel\overline{AD}

, let BC\equal{}1000 and AD\equal{}2008. Let \angle A\equal{}37^\circ, \angle D\equal{}53^\circ, and

m

and

n

be the midpoints of

\overline{BC}

and

\overline{AD}

, respectively. Find the length

MN