The Inscribed Angle Theorem: The Geometry Of Circles

Inscribed Angle

Angle whose vertex lieson a circle and whosesides contain chords ofthe circle

An inscribed angle is an angle formed by two chords in a circle that have a common endpoint, called the vertex, and the vertex is located on the circumference of the circle.

In other words, an inscribed angle is an angle formed by two intersecting chords inside the circle and its vertex lies on the circumference of the circle.

The measure of an inscribed angle is half the measure of the arc that it intercepts. This is known as the Inscribed Angle Theorem.

There are a few important things to note about inscribed angles:

– If an angle is inscribed in a semicircle, it is a right angle (90 degrees).
– If two inscribed angles intercept the same arc, then they have the same measure.
– If a diameter of the circle is drawn, then the angle formed by any chord and the diameter that intersects it is a right angle. This is known as the Diameter-Angle Theorem.

Inscribed angles are commonly used in geometry problems involving circles, such as finding the length of a chord or the measure of an angle.

More Answers: