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angle bisectors intersect at right angles on AD, AB// DC, BC =AB+ CD

Source: 2019 Irish Mathematical Olympiad paper 1 p3

October 5, 2020
geometryangle bisectorconcurrency

Problem Statement

A quadrilateral ABCDABCD is such that the sides ABAB and DCDC are parallel, and ∣BC∣=∣AB∣+∣CD∣|BC| =|AB| + |CD|. Prove that the angle bisectors of the angles ∠ABC\angle ABC and ∠BCD\angle BCD intersect at right angles on the side ADAD.
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