# 10.1 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Use Properties...

date post

12-Jan-2016Category

## Documents

view

216download

1

Embed Size (px)

### Transcript of 10.1 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Use Properties...

Slide 1or area of a circle?

2. Find the radius of a circle with diameter 8 centimeters.

3. A right triangle has legs with lengths 5 inches and

12 inches. Find the length of the hypotenuse.

ANSWER

5. Solve (x + 18)2 = x2 + 242.

ANSWER

3

ANSWER

7

10.1

SOLUTION

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

AC

a.

AC

is a radius because C is the center and A is a point on the circle.

a.

AB

b.

AB

is a diameter because it is a chord that contains the center C.

b.

10.1

SOLUTION

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

DE

c.

is a tangent ray because it is contained in a line that intersects the circle at only one point.

DE

c.

AE

d.

is a secant because it is a line that intersects the circle in two points.

AE

d.

10.1

1. In Example 1, what word best describes AG? CB?

2. In Example 1, name a tangent and a tangent segment.

ANSWER

Radius of A

a.

b.

c.

d.

10.1

Guided Practice

3. Use the diagram in Example 2 to find the radius and diameter of

C and D.

Example 3

Tell how many common tangents the circles have and draw them.

SOLUTION

a.

a.

Example 3

Tell how many common tangents the circles have and draw them.

SOLUTION

b.

Example 3

Tell how many common tangents the circles have and draw them.

SOLUTION

c.

c.

Guided Practice

Tell how many common tangents the circles have and draw them.

4.

Guided Practice

Tell how many common tangents the circles have and draw them.

5.

Guided Practice

Tell how many common tangents the circles have and draw them.

no common tangents

SOLUTION

Use the Converse of the Pythagorean Theorem. Because 122 + 352 = 372, PST is a right triangle and ST PT . So, ST is perpendicular to a radius of P at its endpoint on P. By Theorem 10.1, ST is tangent to P.

In the diagram, PT is a radius of P. Is ST tangent to P ?

10.1

100r = 3900

Divide each side by 100.

In the diagram, B is a point of tangency. Find the radius r of C.

You know from Theorem 10.1 that AB BC , so ABC is a right triangle. You can use the Pythagorean Theorem.

10.1

Solve for x.

RS is tangent to C at S and RT is tangent to C at T. Find the value of x.

Tangent segments from the same point are .

10.1

ANSWER

Yes

10.1

8. ST is tangent to Q.Find the value of r.

10.1

10.1

CD

a.

AB

b.

FD

c.

EP

d.

ANSWER

tangent

ANSWER

chord

ANSWER

radius

10.1

ANSWER

One tangent; it is a vertical line through the point of tangency.

2.

10.1

3.

Yes; 16 + 30 = 1156 = 34 so AB AC, and a line to a radius at its endpoint is tangent to the circle.

2

2

2

ANSWER

10.1

2. Find the radius of a circle with diameter 8 centimeters.

3. A right triangle has legs with lengths 5 inches and

12 inches. Find the length of the hypotenuse.

ANSWER

5. Solve (x + 18)2 = x2 + 242.

ANSWER

3

ANSWER

7

10.1

SOLUTION

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

AC

a.

AC

is a radius because C is the center and A is a point on the circle.

a.

AB

b.

AB

is a diameter because it is a chord that contains the center C.

b.

10.1

SOLUTION

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

DE

c.

is a tangent ray because it is contained in a line that intersects the circle at only one point.

DE

c.

AE

d.

is a secant because it is a line that intersects the circle in two points.

AE

d.

10.1

1. In Example 1, what word best describes AG? CB?

2. In Example 1, name a tangent and a tangent segment.

ANSWER

Radius of A

a.

b.

c.

d.

10.1

Guided Practice

3. Use the diagram in Example 2 to find the radius and diameter of

C and D.

Example 3

Tell how many common tangents the circles have and draw them.

SOLUTION

a.

a.

Example 3

Tell how many common tangents the circles have and draw them.

SOLUTION

b.

Example 3

Tell how many common tangents the circles have and draw them.

SOLUTION

c.

c.

Guided Practice

Tell how many common tangents the circles have and draw them.

4.

Guided Practice

Tell how many common tangents the circles have and draw them.

5.

Guided Practice

Tell how many common tangents the circles have and draw them.

no common tangents

SOLUTION

Use the Converse of the Pythagorean Theorem. Because 122 + 352 = 372, PST is a right triangle and ST PT . So, ST is perpendicular to a radius of P at its endpoint on P. By Theorem 10.1, ST is tangent to P.

In the diagram, PT is a radius of P. Is ST tangent to P ?

10.1

100r = 3900

Divide each side by 100.

In the diagram, B is a point of tangency. Find the radius r of C.

You know from Theorem 10.1 that AB BC , so ABC is a right triangle. You can use the Pythagorean Theorem.

10.1

Solve for x.

RS is tangent to C at S and RT is tangent to C at T. Find the value of x.

Tangent segments from the same point are .

10.1

ANSWER

Yes

10.1

8. ST is tangent to Q.Find the value of r.

10.1

10.1

CD

a.

AB

b.

FD

c.

EP

d.

ANSWER

tangent

ANSWER

chord

ANSWER

radius

10.1

ANSWER

One tangent; it is a vertical line through the point of tangency.

2.

10.1

3.

Yes; 16 + 30 = 1156 = 34 so AB AC, and a line to a radius at its endpoint is tangent to the circle.

2

2

2

ANSWER

10.1

*View more*