OMM 1990 Problem 2

$ABC$ is a triangle with $\angle B = 90^o$ and altitude $BH$ . The inradii of $ABC, ABH, CBH$ are $r, r_1, r_2$ . Find a relation between them.

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.