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Classifying Angles with Circles

Classifying Angles with Circles. Case 1: Vertex is on the circle. a. b. Classifying Angles with Circles. Case 2: Vertex is inside the circle. Classifying Angles with Circles. Case 3: Vertex is outside the circle. a. b. c. . Theorem.

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Classifying Angles with Circles

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  1. Classifying Angles with Circles • Case 1: Vertex is on the circle. a. b.

  2. Classifying Angles with Circles • Case 2: Vertex is inside the circle.

  3. Classifying Angles with Circles • Case 3: Vertex is outside the circle. a. b.

  4. c.

  5. Theorem • If a tangent and a secant (or a chord) intersect ONa circle at the point of tangency, then the measure of the angle formed is one half the measure of its intercepted arc.

  6. Theorem The measure of an angle formed by two secants or chords that intersect in the interior of a circle is one-half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

  7. Theorem • The measure of an angle formed by two secants intersecting in the exterior of a circle is one-half the difference of the measures of the intercepted arcs.

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