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Inscribed Angles

Understand inscribed angles, intercepted arcs, corollaries, and tangents in circles. Solve angle measures using the theorems presented.

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Inscribed Angles

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  1. Inscribed Angles

  2. 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.

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

  4. What is mA?

  5.  What are mA, mB, mC, and mD?

  6. 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.

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

  8.  What is the measure of each numbered angle?

  9. 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.

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

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

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