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|AB|= |CD| or |AB| +|CD| =|AD| in a trapezoid

Source: Dutch BxMO TST 2011 p5

August 3, 2019
geometrytrapezoidangle bisector

Problem Statement

A trapezoid ABCDABCD is given with BC//ADBC // AD. Assume that the bisectors of the angles BADBAD and CDACDA intersect on the perpendicular bisector of the line segment BCBC. Prove that ∣AB∣=∣CD∣|AB|= |CD| or ∣AB∣+∣CD∣=∣AD∣|AB| +|CD| =|AD|.
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