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11.3: Inscribed angles

11.3: Inscribed angles. Objectives: Students will be able to… Apply the relationship between an inscribed angle and the arc it intercepts Find the measures of an angle formed by a tangent and a chord. Inscribed Angle Theorem. Inscribed Angle: sides are chords, vertex is on the circle

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11.3: Inscribed angles

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  1. 11.3: Inscribed angles Objectives: Students will be able to… Apply the relationship between an inscribed angle and the arc it intercepts Find the measures of an angle formed by a tangent and a chord

  2. Inscribed Angle Theorem • Inscribed Angle: sides are chords, vertex is on the circle THEOREM: The measure of an inscribed angle is half the measurement of the intercepted arc

  3. Find the value of each variable. b° a° 60° 108° c°

  4. Corollaries to Inscribed Angle Theorem • 2 inscribed angles that intercept the same arc are congruent • An angle inscribed in a semicircle is a right angle • The opposite angles of a quadrilateral inscribed in a circle are supplementary.

  5. Find the values of the variables 100° c° b° 99° 96° d° a°

  6. Find the value of the variables 1. 2. [ a° P a° 40° b° P is the center of the circle.

  7. Theorem The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc

  8. Example: Find x.

  9. Find the value of a. 300° a°

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