12-3 Inscribed Angles.

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Presentation transcript:

12-3 Inscribed Angles

Inscribed Angles An angle whose vertex is ON the circle and whose sides are chords of the circle is an inscribed angle. An arc whose endpoints are on the inscribed angle is an intercepted arc. Inscribed Angle Theorem: The measure of an inscribed angle is half the measure of its intercepted arc.

Using the Inscribed Angle Theorem What are the values of a and b?

What is mA?

 What are mA, mB, mC, and mD?

Corollaries to the Inscribed Angle Theorem 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.

Using Corollaries to Find Angle Measures What is the measure of each numbered angle?

 What is the measure of each numbered angle?

Tangents and Intercepted Arcs Theorem 12-12: The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc.

Using Arc Measure In the diagram, SR is a tangent to the circle at Q. If mPMQ = 212˚, what is mPQR?

 If KJ is tangent to O, what are the values of x and y?