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Inscribed Angles and Arcs in a Circle

This text provides an introduction to inscribed angles, intercepted arcs, and theorems related to them in the context of circle geometry. It also includes practice problems and assignments.

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Inscribed Angles and Arcs in a Circle

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  1. Week 1 Warm Up 03.23.12

  2. An angle whose vertex is on a circle and whose sides contain chords. Inscribed Angles Intercepted Arc Arc that lies in the interior of an inscribed angle.

  3. Theorem 10.8

  4. Ex 1 a. 180° b. 230° c. 50°

  5. Ex 2 What is the measure of each inscribed angle? Red? 30° Green? 30° 30° Blue?

  6. Theorem 10.9 If two inscribed angles of a circle intercept the same arc, then the angles are congruent.

  7. Find the value of x. Ex 3

  8. Theorem 10.10 If a right triangle is inscribed in a circle, then its hypotenuse is a diameter.

  9. Theorem 10.11 A quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary. 98° 82°

  10. Do 1: Find the value of x. Assignment: Handout – 10.3A Due at the end of the hour.

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