10.1– use properties of tangents

10.1– Use Properties of Tangents

Term Definition Picture

Circle

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

Term Definition Picture

Center

Point equidistant from the sides of the circle. Gives the name of the circle.

P

P

Term Definition Picture

Radius

A segment with endpoints at the center and on the circle P

PQ

Q

Term Definition Picture

Chord

A segment with both endpoints on the circle

P

AQ

QA

Term Definition Picture

Diameter

A segment with both endpoints on the circle that goes through the center of the circle

P

QR

Q

R

Term Definition Picture

Secant

A line that intersects a circle in two points.

P

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Q

R

Term Definition Picture

Tangent

A line that intersects a circle in exactly one point.

P

QR�������������� �

QR

Term Definition Picture

Point of Tangency

The point where a tangent line touches a circle

P

QR S

S

Term Definition Picture

Common Internal Tangent

A line that is tangent inside two circles.

Term Definition Picture

Common External Tangent

A line that is tangent outside two circles.

Term Definition Picture

Coplanar Circles

Two circles on the same plane

Term Definition Picture

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.

tangentperpendicular

Tangent segments from a common ____________ point are ___________________.external congruent

A

B

C

AC AB

1. State the best term for the given figure.

C

center

1. State the best term for the given figure.

Common internal tangent

FE�������������� �

1. State the best term for the given figure.

radius

HG

1. State the best term for the given figure.

chord

DB

1. State the best term for the given figure.

Point of Tangency

F

1. State the best term for the given figure.

diameter

BE

1. State the best term for the given figure.

secant

DB�������������� �

1. State the best term for the given figure.

Common External Tangent

AG�������������� �

2. Find the radius of .A

2u

3. Find the diameter of .B

4u

4. Find the center of .C

(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.

BC .CAB .C

c2 = a2 + b2

52 = 32 + 42

25 = 9 + 16

25 = 25

Right Triangle

Yes

c2 = a2 + b2

192 = 82 + 162

361 = 64 + 256

361 > 320

Not a Right Triangle

NO

6. In the diagram, is a radius of Determine whether is tangent to Explain your reasoning.

BC .CAB .C

7. Given the picture, find the indicated length.

c2 = a2 + b2

802 = a2 + 482

6400 = a2 + 2304

4096 = a2

64a

Given the picture, find the indicated length.

c2 = a2 + b2

252 = x2 + 122

625 = x2 + 144

481 = x2

481 x

6

Given the picture, find the indicated length.Given the picture, find the indicated length.

c2 = a2 + b2

(r + 2)2 = r2 + 42

r2 + 4r + 4 = r2 + 16

4r + 4 = 16

4r = 12

r = 3

(r + 2)(r + 2) = r2 + 16

r2 + 2r + 2r + 4 = r2 + 16

Given the picture, find the indicated length.

c2 = a2 + b2

(r + 9)2 = r2 + 152

r2 + 18r + 81 = r2 + 225

18r + 81 = 225

18r = 144

r = 8

(r + 9)(r + 9) = r2 + 225

r2 + 9r + 9r + 81 = r2 + 225

c2 = a2 + b2

(r + 16)2 = r2 + 242

r2 + 32r + 256 = r2 + 57632r + 256 = 576

32r = 320r = 10

(r + 16)(r + 16) = r2 + 576r2 + 16r + 16r + 256 = r2 + 576

10.1 655-657 3-10, 15-23 odd, 24, 27, 28

HW Problem

#21