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circles. 10.1 Tangents to Circles. Circle Radius Diameter Chord Secant Tangent. Write the following down. Tangent. Circle. Radius. Diameter. Chord. Secant. Based on the picture write your own definitions….

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Circles

circles

10.1 Tangents to Circles


Write the following down

  • Circle

  • Radius

  • Diameter

  • Chord

  • Secant

  • Tangent

Write the following down


Based on the picture write your own definitions

Tangent

Circle

Radius

Diameter

Chord

Secant

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.

Share your thoughts…


Circles

Circle –

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

Radius –

distance from the center to a point on a circle.

Diameter –

the distance across a circle through the center.


Circles

  • Chord –

  • a segment whose endpoints are on the circle.

  • Is the diameter a chord?

  • Yes, but it passes through the center of the circle.


Circles

  • Secant –

  • a line that intersects a circle in two points.

  • Tangent –

  • a line that intersects a circle at exactly one point.


Congruent

2

2

Congruent?


Circles

c

AD

CD

d


Common tangents

k

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

D

C

j

m

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

A

B

Common Tangents

n





Is the segment tangent to the circle

16 point.

12

20

Is the segment tangent to the circle?


Pythagorean thm

  • 144 + 256 = 400 point.

  • It’s a right triangle!

  • So the segment is

    perpendicular.

    So the segment is tangent.

16

12

20

Pythagorean thm.


Is the segment tangent to the circle1

10 point.

12

15.5

Is the segment tangent to the circle?


Pythagorean thm1

10

12

15.5

Pythagorean thm.


Find the radius given that bc is tangent to the circle and therefore perpendicular to the radius

B point.

16 ft

r

C

A

r

8 ft

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


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



Draw if two segments from the same exterior point are tangent to a circle then they are congruent

A point.

C

B

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

CA = CB


Find x

2x + 10 point.

4x - 15

Find x


Find x1

2x + 10

4x - 15

Find x


Homework

Homework point.

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