GMT and inscribed angle

The inscribed angle theorem states that an angle inscribed in a circle is half the measure of the central angle that subtends the same arc. The Geometric Mean Theorem (also called the Right Triangle Altitude Theorem) relates the altitude to the hypotenuse in a right triangle: if an altitude is drawn from the right angle to the hypotenuse, it divides the hypotenuse into two segments, and the length of the altitude is the geometric mean of those two segments.

Important properties

• The measure of an inscribed angle is half the measure of the central angle subtending the same arc.

• All inscribed angles subtending the same arc are equal.

• The Geometric Mean Theorem: In a right triangle, the altitude to the hypotenuse is the geometric mean of the two segments it creates.