9.1 – 9.2 Exploring Circles Geometry

Objectives/Assignment Find the circumference of a circle Use circumference to solve other problems

Definitions Circle – is the set of all points in a plane that are equidistance from a given point on that plane Center- “The given“ point on the plane Radius- A segment that has one endpoint at the center of a circle and the other end point on the circle itself

Definitions Chord – A segment that has both endpoint on a circle Diameter - Is a chord that contains the center of the circle. Circumference - The distance around the circle

Finding circumference The circumference of a circle is the distance around the circle. For all circles, the ratio of the circumference to the diameter is the same. This ratio is known as  or pi.

Circumference of a Circle The circumference C of a circle is C = d or C = 2r, where d is the diameter of the circle and r is the radius of the circle.

Example #1

Example # 2 Find a. the circumference of a circle with radius 6 centimeters b. the radius of a circle with circumference 31 meters.

Solution: C = 2r = 2 •  • 6 = 12  37.70 b. a. C = 2r = 2 •  • 6 = 12  37.70 So, the circumference is about 37.70 cm. C = 2r 31 = 2r 31 = r 4.93  r So, the radius is about 4.93 cm. 2

Practice

Take Notes

Take Notes C = 2 *3.14* 7 = 44 D = 2 * r = 14 C = 2 *3.14* 16.2 = 101.8 R = D / 2 = 16.2

Take Notes 116.5 = 2 * 3.14 * r 116.5 = 6.28 * r R = 18.6 D = 2 * r = 18.6 * 2 = 37.1

Take Notes C = 2 * 3.14 * 12 C = 6.28 * 12 C = 75.4 D = 2 * r = 2* 12 = 24

Take Notes D² = 5² + 5² D² = 10² + 24² D² = 25 +25 C = 2 * 3.14 * 14

And… Sum Of Central Angles

Practice

4x + 35 = 9x +5 30 = 5x X = 6 AE = = 4 * 6 + 35 = 59 ED = = 9 * 6 + 5 = 59 ے 1 + ے 2 + ے 3 = 180 , 180- 59- 59 = 62 ے 3 = ے 4 ( vertical) = 62 ے 1 + ے 3 = 59 + 62 = 121 ے 4 + ے 2 = 59+ 62 = 121

360 - ے 1 + ے 2 + ے 3 + ے4 , 360-59-59-62-62 = 118 = = 118 ے 1 + ے 2 + ے 3 + ے4 = 242 DC =ے 3 = 62 ے 1 + ے 2 + ے 3 = 180