MathDB
Trapezoid

Source: 22nd Hellenic Jounior mo , 2005 , prb1.

November 17, 2005
geometrytrapezoid

Problem Statement

We are given a trapezoid ABCDABCD with AB∥CDAB \parallel CD, CD=2ABCD=2AB and DB⊥BCDB \perp BC. Let EE be the intersection of lines DADA and CBCB, and MM be the midpoint of DCDC. (a) Prove that ABMDABMD is a rhombus. (b) Prove that triangle CDECDE is isosceles. (c) If AMAM and BDBD meet at OO, and OEOE and ABAB meet at N,N, prove that the line DNDN bisects segment EBEB.
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