A circle with centre O has two chords drawn inside it: chord AB and chord CD. You can drag all four endpoints around the circle. From the centre, a perpendicular segment is drawn to each chord, giving its distance from the centre. The theorem: two chords are equal in length exactly when they are the same distance from the centre — and the longer a chord is, the closer it lies to the centre. Each chord's length and its distance from the centre are shown live, linked by length equals two times the square root of radius squared minus distance squared. A button can make the second chord equal to the first. An info button opens a drawer with the explanation.
equal chords ⟺ equal distance from O (length = 2√(R² − d²))