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CA =CD wanted, <CBD = 90^o,<BCD =<CAD, AD=2BC (2020 Kyiv City MO Round2 8.2)

Source:

September 21, 2020
geometryequal segmentsequal anglesright angle

Problem Statement

Given a convex quadrilateral ABCDABCD, in which ∠CBD=90o\angle CBD = 90^o, ∠BCD=∠CAD\angle BCD =\angle CAD and AD=2BCAD= 2BC. Prove that CA=CDCA =CD.
(Anton Trygub)
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