*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