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Lesson 9-3

Lesson 9-3. Arcs and Central Angles. Central Angle. Definition:. An angle whose vertex lies on the center of the circle. NOT A Central Angle (of a circle). Central Angle (of a circle). Central Angle (of a circle). Y. 110 . 110 . O. Z. Central Angle Theorem.

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Lesson 9-3

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  1. Lesson 9-3 Arcs and Central Angles

  2. Central Angle Definition: An angle whose vertex lies on the center of the circle. NOT A Central Angle (of a circle) Central Angle (of a circle) Central Angle (of a circle)

  3. Y 110 110 O Z Central Angle Theorem The measure of a center angle is equal to the measure of the intercepted arc. Center Angle Intercepted Arc Example: is the diameter, find the value of x and y and z in the figure.

  4. Example: Find the measure of each arc. 4x + 3x + (3x +10) + 2x + (2x-14) = 360° 14x – 4 = 360° 14x = 364° x = 26° 4x = 4(26) = 104° 3x = 3(26) = 78° 3x +10 = 3(26) +10= 88° 2x = 2(26) = 52° 2x – 14 = 2(26) – 14 = 38°

  5. Measures of an Arc Measures of an Arc: 1. The measure of a minor arc is the measure of its central angle. 2. The measure of a major arc is 360 - (measure of its minor arc). 3. The measure of any semicircle is 180. Adjacent Arcs: Arcs in a circle with exactly one point in common. List: Major Arcs Minor Arcs Semicircles Adjacent Arcs

  6. Theorem • In the same circle or in congruent circles, two minor arcs are congruent if and only if their central angles are congruent.

  7. Arc Addition Postulate • The measure of the arc formed by two adjacent arcs is the sum of the measures of these two arcs.

  8. Example • In circle J, find the measures of the angle or arc named with the given information: • Find:

  9. In Circle C, find the measure of each arc or angle named. • Given: SP is a diameter of the circle. Arc ST = 80 and Arc QP=60. • Find:

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