The namesake of this website is…
Angle Inscribed in a Semicircle Theorem:
An angle inscribed in a semicircle is a right angle.
Equivalent forms:
- If an angle is inscribed in a semicircle, then it is a right angle.
- If an angle is determined by the endpoints of a diameter and a third point on the circle, as the vertex, then the angle is a right angle.
Converse:
An inscribed angle which is a right angle is inscribed in a semicircle.
Equivalent form:
- If a right angle is an inscribed angle of a circle, then it is inscribed in a semicircle.
- If a right angle, ∠ABC, is an inscribed angle of a circle, then segment AB is a diameter of the circle.
This may be my favorite theorem in mathematics!
Jim Olsen
See example at http://www.mathopenref.com/semiinscribed.html