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another problem about trapezoids

Source: Romanian TST 1978, Day 3, P1

September 30, 2018
geometryperimetertrapezoidPure geometry

Problem Statement

In a convex quadrilateral ABCD, ABCD, let A’,B’ A’,B’ be the orthogonal projections to CD CD of A, A, respectively, B. B.
a) Assuming that BB’≤AA’ BB’\le AA’ and that the perimeter of ABCD ABCD is (AB+CD)⋅BB’, (AB+CD)\cdot BB’, is ABCD ABCD necessarily a trapezoid? b) The same question with the addition that ∠BAD \angle BAD is obtuse.
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