Let $ABC$ be a right triangle with leg $CB = 2$ and hypotenuse $AB= 4$. Point $K$ is chosen on the hypotenuse $AB$, and point $L$ is chosen on the leg $AC$. a) Describe and justify how to construct such points $K$ and $ L$ so that the sum of the distances $CK+KL$ is the smallest possible. b) Find the smallest possible value of $CK+KL$. (Olexii Panasenko)
Problem
Source: 2022 Yasinsky Geometry Olympiad X-XI p5 , Ukraine
Tags: geometry, geometric inequality, right triangle