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CHAPTER
6.1 Circles and Arcs
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Circles
In a plane, a circle is the set of all points equidistant from a given point called the center. We name a circle by its center. Circle P is shown below.
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Circles
A diameter is a segment that contains the center of a circle and has both endpoints on the circle. A radius is a segment that has one endpoint at the center and the other endpoint on the circle. Congruent circles have congruent radii. A central angle is an angle whose vertex is the center of the circle.
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Theorem 6.1
Therep 
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Congruent Circles
If two circles are congruent, then their radii and diameters are congruent. Conversely, if the radii or diameters are congruent, then two circles are congruent.
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Circles
An arc is a part of a circle. One type of arc, a semicircle, is half of a circle. A minor arc is smaller than a semicircle. A major arc is larger than a semicircle. We name a minor arc by its endpoints and a major arc or a semicircle by its endpoints and another point on the arc.
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Central Angle
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Arc Measure
The measure of an Arc is the number of degrees in the central angle that intercepts the arc.
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Congruent Arcs
Congruent arcs are arcs that have the same measure and are in the same circle or in congruent circles.
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10. Postulate 6.2 Arc Addition Postulate
The measure of the arc formed by two adjacent arcs is the sum of the measures of the two arcs.
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Arc Measure
• minor arc—The measure of a minor arc is equal to the measure of its corresponding central angle. • major arc—The measure of a major arc is the measure of the related minor arc subtracted from 360°. • semicircle—The measure of a semicircle is 180°.
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12. Finding the Measures of Arcs
What is the measure of each arc in circle O? a. b. c. d. Solution a. b.
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13. Finding the Measures of Arcs
What is the measure of each arc in circle O? a. b. c. d. Solution c.
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Arc
• A semicircle is half of a circle. • A minor arc is smaller than a semicircle. • A major arc is larger than a semicircle.
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Inscribed Angle
An angle whose vertex is on a circle and whose sides intersect the circle in two other points is called an inscribed angle. Thm 6.2 – The measure of an inscribed angle is one-half the measure of its intercepted arc.
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Corollaries
Corollary 6.3 – Inscribed angles that intercept the same or congruent arcs are congruent Corollary 6.4 – Every angle inscribed in a semicircle is a right angle
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