Interactive resource
Hidden circle II: angle in a semicircle
Geometry. Right angles subtended by a segment lie on the circle with that diameter. Free interactive GeoGebra resource — adjust parameters in the browser.
Overview
Right angles subtended by a segment lie on the circle with that diameter.
Explanation
Thales: ∠APB = 90° ⇔ P lies on the circle with diameter AB (P ≠ A, B).
Corollary: the median to the hypotenuse is half the hypotenuse.
“Right angle + hypotenuse” suggests the diameter circle.
How to use
Drag P with ∠APB = 90°; median OP stays half of AB.