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MathNet 2021 — Part 07 Question 58

Math Olympiad Vault · MathNet 2021 — Part 07

Question 58

Let $ABCD$ be a convex quadrilateral such that $AB + BC = 2021$ and $AD = CD$. We are also given that
$$\angle ABC = \angle CDA = 90^{\circ}$$
Determine the length of the diagonal $BD$.