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concurrency of perp. bisectors (2020 Kyiv City MO 7.4.1)

Source:

September 19, 2020
geometryconcurrencyconcurrentperpendicular bisectorequal segments

Problem Statement

In the quadrilateral ABCDABCD, AB=BCAB = BC . The point EE lies on the line ABAB is such that BD=BEBD= BE and AD⊥DEAD \perp DE. Prove that the perpendicular bisectors to segments AD,CDAD, CD and CECE intersect at one point.
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