MathDB

4

Part of 2008 Greece Junior Math Olympiad

Problems(1)

trapezoid with 2 right angles, concurrency wanted (Greece Junior 2008)

Source:

7/14/2019
Let ABCDABCD be a trapezoid with AD=a,AB=2a,BC=3aAD=a, AB=2a, BC=3a and ∠A=∠B=90o\angle A=\angle B =90 ^o. Let E,ZE,Z be the midpoints of the sides AB,CDAB ,CD respectively and II be the foot of the perpendicular from point ZZ on BCBC. Prove that : i) triangle BDZBDZ is isosceles ii) midpoint OO of EZEZ is the centroid of triangle BDZBDZ iii) lines AZAZ and DIDI intersect at a point lying on line BOBO
geometrytrapezoidisoscelesconcurrent