Inscribed AnglesBy the end of today, you will know what an

inscribed angle is and how to find its measure.

An inscribed angle is an angle whose vertex is on a circle.

Inscribed Angle

The arc that lies in the interior of an inscribed angle and has endpoints on the angle.

Intercepted Arc

The measure of an inscribed angle is half the measure of its intercepted arc.

Measure of an Inscribed Angle Theorem

Theorem 10.8

If two inscribed angles of a circle intercept the same arc, then the angles are congruent.

Inscribed Polygon

A polygon is an inscribed polygon if all of its vertices lie on a circle.

The circle that contains the vertices is circumscribed circle.

If a right triangle is inscribed in a circle, then the hypotenuse is a diameter of the circle. Conversely, if one side of an inscribed triangle is a diameter of the circle, then the triangle is a right triangle and the angle opposite the diameter is the right angle.

Theorem 10.9

A quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary.

Theorem 10.10

Inscribed vs. Central Angles

If the measure of an inscribed angle is 60o, what is the measure of its intercepted arc?

If the measure of a central angle is 60o, what is the measure of its intercepted arc?

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Assignment