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Warm up

Warm up. 3x = x + 50 y + 5y + 66 = 360 x +14x = 180 a ² + 16 = 25. Homework Quiz (TI). The radius of a circle is given. Find the diameter. 13 ft. 2. 3.2 in Tell whether AB is tangent to circle C. 3. B. A. 80. 18. C. 82. Arcs and Chords. Chapter 10 Section 2. A. P. B.

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Warm up

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  1. Warm up • 3x = x + 50 • y + 5y + 66 = 360 • x +14x = 180 • a² + 16 = 25

  2. Homework Quiz (TI) • The radius of a circle is given. Find the diameter. • 13 ft. 2. 3.2 in • Tell whether AB is tangent to circle C. 3. B A 80 18 C 82

  3. Arcs and Chords Chapter 10 Section 2

  4. A P B Central Angle • A central angle is an angle whose vertex is the center of a circle. Central Angle: <APB

  5. A P B Arc • An arc is an unbroken piece of a circle. • A central angle divides a circle into two arcs. Arc AB is a minor arc because it is less than ½ of the circle (180°) Arc ACB is a major arc because it measures more than 180°. (more than ½ the circle) You must name it using 3 letters!!! C

  6. Semicircle • A semicircle is an arc that is exactly ½ the circle (180 degrees). • It is formed by a diameter of a circle. • It is named using three letters. B A O D

  7. A P B Measure of an Arc • Arcs are measured in degrees. • A circle contains 360 degrees. • A minor arc has the same measure as its central angle. • A major arc’s measure is 360 minus its central angle. mAB = m<APB mAB = 60° 60° mACB = 360 – 60 = 300° A semicircle always equals 180 degrees! C

  8. Find the measure of each arc below. B CD = CDB = BCD = C A 148° D

  9. P O T W Adjacent arcs • Adjacent arcs are arcs that intersect in exactly one point. • The measure of an arc formed by two adjacent arcs can be found by adding the two adjacent arcs. 45° 55°

  10. 45 45 Congruent arcs • Two arcs of the same circle or congruent circles are congruent if they have the same measure. A C 50° B 50° D

  11. X W 30° Z Y

  12. Theorem • In the same circle or in congruent circles, two minor arcs are congruent iff their corresponding chords are congruent. AB is congruent to CD because AB is congruent to CD. B A C D

  13. EXAMPLE • Find the measure of arc BC. B (2x + 48) (3x + 11) A D C

  14. Theorem • If a diameter of a circle is perpendicular to a chord, then it bisects the chord and its arc. The converse of this theorem is true too.

  15. Theorem • In the same circle or congruent circles, two chords are congruent iff they are equidistant from the center of the circle. RT = SQ BECAUSE they are the same distance from the center of the circle. R T Q S

  16. example • AB = 12, DE = 12, and CE = 7. Find CG. B G A C D F E

  17. Complete Assignment #2

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