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The Theorem

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