A right triangle ABC has its right angle at C. The vertex C stays on the circle whose diameter is the hypotenuse AB, which keeps the angle at C exactly 90 degrees. An altitude is dropped from C straight down to the hypotenuse, meeting it at foot D and splitting the hypotenuse into two parts: p from A to D and q from D to B. Three geometric-mean relations hold: the altitude squared equals p times q; leg AC squared equals p times the whole hypotenuse; leg BC squared equals q times the whole hypotenuse. You can drag A and B along the base and drag C around the circle. All three relations are shown live and stay true. An info button opens a drawer with the explanation.