circles10.1 Tangents to Circles

Write the following down

• Circle• Radius• Diameter• Chord• Secant• Tangent

Tangent

Radius

Diameter

Chord

Secant

Circle

Based on the picture write your own definitions…

Share your thoughts…

• Talk to the person NEXT TO YOU about what you got for each of your definitions.• Change your definition based on your

conversations.

Circle –a set of all points in a plane that are equidistant from a given pointRadius – distance from the center to a point on a circle.Diameter – the distance across a circle through the center.

• Chord – • a segment whose endpoints are on the

circle.• Is the diameter a chord?• Yes, but it passes through the center of the

circle.

• Secant – • a line that intersects a circle in two

points.• Tangent – • a line that intersects a circle at exactly

one point.

Congruent?

• Draw two congruent circles.• What property do they share?• Circles are congruent if they have the

same radius.

2 2

c

dCD

AD

Common Tangents

CD

k

j

BA

n

m

Common Internal Tangent – Intersects the segment that joins the centers of the two circles.

Common External Tangent – Does not intersect the segment that joins the centers of the two circles.

Are these lines tangent to the circle???

What can you conclude about tangent lines and the radius at the same pt.?

Tangent lines are perpendicular to the radius at the same point.

Is the segment tangent to the circle?

12

16

20

Pythagorean thm.

• 144 + 256 = 400• It’s a right triangle!• So the segment is perpendicular.So the segment is tangent.

12

16

20

Is the segment tangent to the circle?

12

10

15.5

Pythagorean thm.

• 144 + 100 = 240.25• not a right triangle• So it’s not perpendicular.

12

10

15.5

Find the radius, given that BC is tangent to the circle, and therefore perpendicular to the radius.

A

B

Cr

r

16 ft

8 ft

When will the purple segment be equal to the corresponding black segment?

Are they equal yet?

Draw! (If two segments from the same exterior point are tangent to a circle, then they are congruent.

A

B

C

CA = CB

Find x

2x + 10

4x - 15

Find x

• 2x + 10 = 4x-15

• 25 = 2x• 12.5 = x

2x + 10

4x - 15

HomeworkPg. 599: 18-28, 36-41, 46-48