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Lesson 6-7 Arcs Length

Lesson 6-7 Arcs Length. TOPIC VII - CIRCLES. Arcs LenGTH. Arc Definition. It is two points on the circle and the continuous (unbroken) part of the circle between the two points. C. Minor arc is an arc that is smaller than a semicircle and are named by their end points. 100 o.

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Lesson 6-7 Arcs Length

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  1. Lesson 6-7ArcsLength TOPIC VII - CIRCLES

  2. ArcsLenGTH ArcDefinition It is two points on the circle and the continuous (unbroken) part of the circle between the two points. C Minor arc is an arc that is smaller than a semicircle and are named by their end points 100o The measure of the minor arc is the measure of the central angle. R o m COR = 100o A CR = 100o

  3. ArcsLenGTH The measure of the arc from 12:00 to 4:00 is equal to the measure of the angle formed by the hour and minute hands A circular clock is divided into 12 equal arcs, so the measure of each hour is 360or 30°. 12

  4. ArcsLenGTH Because the minute hand is longer, the tip of the minute hand must travel farther than the tip of the hour hand even though they both move 120° from 12:00 to 4:00. So the arc length is different even though the arc measure is thesame!

  5. ArcsLenGTH The arc measure is 90°, a full circle measures 360°, and 90° = 1. 360° 4 The arc measure is half of thecircle because180° = 1 360° 2 The arc measure is one-third of thecirclebecause120° = 1 360° 3 The arc length is some fraction of the circumference of its circle.

  6. ArcsLenGTH To find the arcs length we have to follow this steps Step 1: find what fraction of the circle each arc Step 2: Find the circumference of each circle Step 3: Combine the circumferences to find the length of the arcs

  7. ArcsLenGTH For AB and CED find what fraction of the circle each arc is Step 1: find what fraction of the circle each arc The arc measure is 90° a full circle measures 360° and 90° = 1. 360° 4 The arc measure is half of thecirclebecause 180° = 1 360° 2

  8. ArcsLenGTH Step 2: Find the circumference of each circle Circle T C = 2(12 m) C= 24 m Circle O C= 2 (4 in.) C= 8  in Step 3: Combine the circumferences to find the length of the arcs Circle T Length of AB= 90° 2 (12m) 360° Or AB= 90° 24 m 360° AB = 18.84 m Circle O Length of CD= 180° 2 (4 in) 360° Or CD= 180° 8 in 360° CD = 12.56 in

  9. ArcsLenGTH ArcLengthconjecture The length of an arc equals the measure of the arc divided by 360° times the circumference l = x . 2 r 3600

  10. ArcsLenGTH Remember: The arc is part of a circle and its length is a part of the circumference of a circle. The measure of an arc is calculated in units of degrees, but arc length is calculated in units of distance (foot, meters, inches, centimeter.

  11. ArcsLenGTH Example:

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