Special Segments in Circles

1 / 15

Special Segments in Circles - PowerPoint PPT Presentation

Special Segments in Circles. Lesson 9.1B R.4.G.5 Investigate and use the properties of angles ( central and inscribed ) arcs , chords , tangents , and secants to solve problems involving circles

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

PowerPoint Slideshow about 'Special Segments in Circles' - fell

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

Special Segments in Circles

Lesson 9.1B

R.4.G.5 Investigate and use the properties of angles (central and inscribed) arcs, chords, tangents, and secants to solve problems involving circles

CGT.5.G.4 Write, in standard form, the equation of a circle given a graph on a coordinate plane or the center and radius of a circle

Vocabulary

Tangent line:

A line that touches the circle at exactly one point.

Tangent line is always perpendicular to the radius

Vocabulary

Secant line:

A line that intersects the circle at exactly two points.

d

b

a

c

The IIII Theorem

If two chords or secant segments intersect inside a circle, then the products of the intersected pieces are congruent

a · b = c · d

8

x

3

6

Example

Find the value of x.

2

11

6

x

Now You Try…

Find the value of x.

Vocabulary

External Secant Segment

The piece of a secant that is between the circle and a point outside the circle.

Tangent Segment

The piece of a tangent line that is between the circle a point outside the circle.

IOIO Theorem

If two secants are drawn from an exterior point to a circle, then the product of the measure of one secant’s external segment with the sum of the internal and external segments is equal to the product of the measure of the other secant’s external segment with the sum of the internal and external segments.

b

d

a

c

b(a+b) = d(c+d)

x

18

6

8

Example

Find the value of x.

9

x

3

4

Now You Try…

Find the value of x.

IOO Theorem

If a secant and tangent are drawn from an exterior point to a circle, then the square of the measure of the tangent segment is equal to the product of the measure of the secant’s external segment with the sum of the internal and external segments

b

a

c

a2 = b(b+c)

12

8

x + 4

Example

Find the value of x.

12

9

x

Now You Try…

Find the value of x.