The distance from the centre to a chord
Problem
A chord $AB$ of length $4$ is drawn in a circle $\omega$ with centre $O$ and radius $\frac{5}{2}$. Find the distance from $O$ to the chord $AB$.
The diagram
Drag any point and the whole construction follows; ▶ runs a point along its circle and back. Tap a point to pin it, double-click to go back to the start. Effects redraws the figure in grayscale for print, in colour, or with the givens in focus.