10.1– Use Properties of Tangents of Circles

TermDefinitionPicture Circle The set of all points in a plane that are equidistant from a given point

TermDefinitionPicture Center Point equidistant from the sides of the circle. Gives the name of the circle. P

TermDefinitionPicture Radius A segment with endpoints at the center and on the circle P Q

TermDefinitionPicture Chord A segment with both endpoints on the circle P Q A

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

TermDefinitionPicture Secant A line that intersects a circle in two points. P Q R

TermDefinitionPicture Tangent A line that intersects a circle in exactly one point. P Q R

TermDefinitionPicture Point of Tangency The point where a tangent line touches a circle P Q R S S

TermDefinitionPicture Common Internal Tangent A line that is tangent inside two circles.

TermDefinitionPicture Common External Tangent A line that is tangent outside two circles.

TermDefinitionPicture Coplanar Circles Two circles on the same plane

TermDefinitionPicture Concentric circles Circles that have the same center

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

Tangent segments from a common ____________ point are ___________________. externalcongruent A B C

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 2u2u

3. Find the diameter of 4u4u

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. 4x + 7 = 7x – 8 7 = 3x – 8 15 = 3x 5 = x

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

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

7. Given the picture, find the indicated length. c 2 = a 2 + b = a = a = a 2

Given the picture, find the indicated length. c 2 = a 2 + b = x = x = x 2 6

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

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

c 2 = a 2 + b 2 (r + 16) 2 = r r r = r r = r = 320 r = 10 (r + 16)(r + 16) = r r r + 16r = r , odd, 24, 27, 28 HW Problem #21