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perpencularities on trapezoid with right angles (Greece Junior 2016)

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July 15, 2019
geometrytrapezoidperpendicularright

Problem Statement

Let ABCDABCD be a trapezoid (AD//BCAD//BC) with ∠A=∠B=90o\angle A=\angle B= 90^o and AD<BCAD<BC. Let EE be the intersection point of the non parallel sides ABAB and CDCD, ZZ be the symmetric point of AA wrt line BCBC and MM be the midpoint of EZEZ. If it is given than line CMCM is perpendicular on line DZDZ, then prove that line ZCZC is perpendicular on line ECEC.
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