Sect Inscribed Angles Geometry Honors

What and Why What? – Find the measure of inscribed angles and the arcs they intercept. Why? – To use the relationships between inscribed angles and arcs in real-world situations, such as motion pictures.

Recall Central Angle A central angle is an angle whose vertex is the center of the circle. The arc formed by a central angle is the same measure as the angle.

Inscribed Angles

Measuring Inscribed Angles

Example

Theorem Inscribed Angle Theorem

There are three cases of this theorem to consider. Case 1: The center is on a side of the angle.

Case 2 The center is inside the angle.

Case 3 The center is outside the angle.

Example Find the values of a and b in the diagram.

Corollaries Corollary 1 – Two inscribed angles that intercept the same arc are congruent. Corollary 2 – An angle inscribed in a semicircle is a right angle. Corollary 3 – The opposite angles of a quadrilateral inscribed in a circle are supplementary.

Examples Find the measure of the numbered angle.

Theorem The measure of an angle formed by a chord and a tangent that intersect on a circle is half the measure of the intercepted arc.

Example