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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: 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 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.
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.
Theorem 10.1 In the same or in congruent circles, two arcs are congruent iff their corresponding central angles are congruent.
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
Ex 1: Find the measure of each arc 58° BC BD ABC AB E) BAD 32°
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
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