MathNet 2022-part-03 — 197 problems (EN–VI) Question 196

In triangle $ABC$, $\angle A$ is a right angle. A point $D$ lies on line segment $AB$ in such a way that the angles $ACD$ and $BCD$ are equal. Moreover, $|AD| = 2$ and $|BD| = 3$.



What is the length of line segment $CD$?