Lesson 6.1 Properties of Tangents

Page 182

Q1 Select A

A.) This is the correct answer.

B.) This is the wrong answer.

C.) This is just as wrong as B

Q2 This time select B

A.) This is the wrong choice.

B.) This is the correct choice.

C.) Do not select this answer.

Circle

• A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle.

Radius

• A radius is a segment whose endpoints are the center and any point on the circle.

Chord

• A chord is a segment whose endpoints are on a circle.

What is special about this one?

• A diameter is a chord that contains the center of the circle.

Secant Tangent• A secant is a line that intersects a circle in two

points.• A tangent is a line in the plane of a circle that

intersects the circle in exactly one point, the point of tangency.

Q3 Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of

circle P.A.) radius

B.) chord

C.) diameter

D.) secant

E.) tangent

RT

Q4 Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of

circle P.A.) radius

B.) chord

C.) diameter

D.) secant

E.) tangent

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Q5 Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of

circle P.A.) radius

B.) chord

C.) diameter

D.) secant

E.) tangent

PT

Q6 Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of

circle P.A.) radius

B.) chord

C.) diameter

D.) secant

E.) tangent

RQ�������������� �

Q7 How many common tangents are possible between the two circles?

A.) 1

B.) 2

C.) 3

D.) 4

E.) 5

Q8 How many common tangents are possible between the two circles?

A.) 1

B.) 2

C.) 3

D.) 4

E.) 5

Q9 How many common tangents are possible between the two circles?

A.) 1

B.) 2

C.) 3

D.) 4

E.) 5

Theorem 6.1:

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

mABC = 90.00

C

B

A

Theorem 6.2:

• Tangent segments from a common external point are congruent.

mDEC = 90.00mABC = 90.00

DC

B

A

E

222 cba

If we show that angle ABC is 90⁰ then segment BC must be a tangent.

222 1068 1003664

100100 So angle ABC is 90⁰ and the segment BC is perpendicular to radius AB.

Example 5

222 cba 222 )50(70 rr

25001004900 22 rrr25002500 22 rr

r1002400 100100r24

Q10 What is the value of r?

A.) 1 cm

B.) 2 cm

C.) 3 cm

D.) 4 cm

E.) 5 cm

mDCB = 90

r

r

BC = 4 cm

AB = 2 cm

A

C

D

B

Homework1-22 page 186

Use the diagram to determine if the statement is true or false.

222 cba 222 )36(48 rr

________________ 22 rrr

Hint

222 cba 222 )1804000(4000 d

Hint