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Central Angles and Arcs

Central Angles and Arcs. Central angles:. A central angle is an angle whose vertex is the center of the circle. ∠APC, ∠CPB and ∠APB Are central angles. Key concept: The sum of the measure of the central angles in a circle is 360°. m ∠1+m∠2+m∠3 = 360°. ARC: Is a part of a circle

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Central Angles and Arcs

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  1. Central Angles and Arcs

  2. Central angles: A central angle is an angle whose vertex is the center of the circle. ∠APC, ∠CPB and ∠APB Are central angles. Key concept: The sum of the measure of the central angles in a circle is 360°. m∠1+m∠2+m∠3 = 360°

  3. ARC: Is a part of a circle THREE TYPES OF A CIRCLE : A) SEMI – CIRCLE (Half a circle) = 180° TRS is a semi-circle mTRS is 180° B) MINOR ARC: shorter than a semi-circle RS is a minor arc mRS = m∠RPS 60° 60° Note: The Measure of a minor arc = the measure of its central angle.

  4. C) Major Arc: Larger than a semi-circle. RTS is a major arc mRTS = 360 – mRS Note: The measure of a major arc is: 360 – the measure of its related minor arc.

  5. Theorem 10.1 In the same or in congruent circles, two arcs are congruent iff their corresponding central angles are congruent.

  6. Adjacent Arcs: two arcs in the same circle that have exactly one point in common. Note: you can add the measures of adjacent arc just like you add the measures of adjacent angles. Arc Addition Postulate: mABC = mAB + mBC

  7. Ex 1: Find the measure of each arc 58° BC BD ABC AB E) BAD 32°

  8. ARC LENGTH: Another way to measure an arc is by its length. Since an arch is a part of a circle, its length is PART of the circumference. Ex: Find the length of XY. Leave your answer in term of π. 16 in

  9. Ex: Find the length of XPY. Leave your answer in terms of π. XPY = 240° Ex: Find the length of a semi – circle in circle P with a radius of 1.3 m. 1.3 m

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