MathNet 2018-part-07 — 177 problems (EN–VI) Question 98

Let $ABCD$ be a convex quadrilateral so that all of its sides and diagonals have integer lengths. Given that $\angle ABC = \angle ADC = 90^{\circ}$, $AB = BD$, and $CD = 41$, find the length of $BC$.

Proposed by: Anders Olsen