10 1 Use Properties of Tangents of Circles

10. 1– Use Properties of Tangents of Circles

Term Definition Circle The set of all points in a plane that are equidistant from a given point Picture

Term Definition Center Point equidistant from the sides of the circle. Gives the name of the circle. Picture P

Term Definition A segment with endpoints at the center and on the circle Radius Picture Q P

Term Chord Definition A segment with both endpoints on the circle Picture Q A P

Term Definition Diameter A segment with both endpoints on the circle that goes through the center of the circle Picture Q P R

Term Secant Definition A line that intersects a circle in two points. Picture Q P R

Term Tangent Definition A line that intersects a circle in exactly one point. Picture P R Q

Term Point of Tangency Definition The point where a tangent line touches a circle Picture P R Q S S

Term Common Internal Tangent Definition A line that is tangent inside two circles. Picture

Term Common External Tangent Definition A line that is tangent outside two circles. Picture

Term Coplanar Circles Definition Two circles on the same plane Picture

Term Definition Circles that Concentric have the circles same center Picture

tangent In a plane, a line is _______ to a circle if and only if the line is __________ to perpendicular a radius of the circle and its endpoint on the circle.

Tangent segments from a common ______ point are __________. external congruent C A B

1. State the best term for the given figure. C center

1. State the best term for the given figure. Common internal tangent

1. State the best term for the given figure. radius

1. State the best term for the given figure. chord

1. State the best term for the given figure. Point of Tangency

1. State the best term for the given figure. diameter

1. State the best term for the given figure. secant

1. State the best term for the given figure. Common External Tangent

2. Find the radius of 2 u

3. Find the diameter of 4 u

4. Find the center of (2, 4)

5. The points K and M are points of tangency. Find the value of x. x = 22

5. The points K and M are points of tangency. Find the value of x. 4 x + 7 = 7 x – 8 7 = 3 x – 8 15 = 3 x 5=x

6. In the diagram, is a radius of Determine whether is tangent to Explain your reasoning. c 2 = a 2 + b 2 52 = 32 + 42 25 = 9 + 16 25 = 25 Right Triangle Yes

6. In the diagram, is a radius of Determine whether is tangent to Explain your reasoning. c 2 = a 2 + b 2 192 = 82 + 162 361 = 64 + 256 361 > 320 Not a Right Triangle NO

7. Given the picture, find the indicated length. c 2 = a 2 + b 2 802 = a 2 + 482 6400 = a 2 + 2304 4096 = a 2

Given the picture, find the indicated length. c 2 = a 2 + b 2 252 = x 2 + 122 6 625 = x 2 + 144 481 = x 2

Given the picture, find the indicated length. c 2 = a 2 + b 2 (r + 2)2 = r 2 + 42 (r + 2) = r 2 + 16 r 2 + 2 r + 4 = r 2 + 16 r 2 + 4 r + 4 = r 2 + 16 4 r + 4 = 16 4 r = 12 r=3

Given the picture, find the indicated length. c 2 = a 2 + b 2 (r + 9)2 = r 2 + 152 (r + 9) = r 2 + 225 r 2 + 9 r + 81 = r 2 + 225 r 2 + 18 r + 81 = r 2 + 225 18 r + 81 = 225 18 r = 144 r=8

HW Problem 10. 1 655 -657 3 -10, 15 -23 odd, 24, 27, 28 #21 c 2 = a 2 + b 2 (r + 16)2 = r 2 + 242 (r + 16) = r 2 + 576 r 2 + 16 r + 256 = r 2 + 576 r 2 + 32 r + 256 = r 2 + 576 32 r + 256 = 576 32 r = 320 r = 10