10.6 Secants, Tangents, & Angle Measures
This presentation is the property of its rightful owner.
Sponsored Links
1 / 18

10.6 Secants, Tangents, & Angle Measures PowerPoint PPT Presentation


  • 109 Views
  • Uploaded on
  • Presentation posted in: General

10.6 Secants, Tangents, & Angle Measures. Objectives. Find measures of angles formed by lines intersecting on, inside, or outside a circle. A. D. O. C. B. Secants and Interior Angles.

Download Presentation

10.6 Secants, Tangents, & Angle Measures

An Image/Link below is provided (as is) to download presentation

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


10 6 secants tangents angle measures

10.6 Secants, Tangents, & Angle Measures


Objectives

Objectives

  • Find measures of angles formed by lines intersecting on, inside, or outside a circle.


Secants and interior angles

A

D

O

C

B

Secants and Interior Angles

Theorem 10.12:If two secants intersect in the interior of a , then the measure of an  formed is ½ the measure of the sum of the arcs intercepted by the secants that created the .

mAOC = ½ (m arc AC + m arc DB)

mAOD = ½ (m arc AD + m arc CB)


Example 1

Find if and

Example 1:

Method 1


Example 11

Example 1:

Method 2

Answer: 98


Your turn

Find if and

Your Turn:

Answer: 138


Secants tangents and angles

D

A

O

C

B

F

Secants, Tangents and Angles

Theorem 10.13:If a secant and a tangent intersect at the point of tangency, then the measure of each  formed is ½ the measure of its intercepted arc.

mDOB = ½ (m arc OB) mCOB = ½ (m arc OFB)


Example 2

Find if and

Example 2:

Answer: 55


Your turn1

Find if and

Your Turn:

Answer: 58


Secants tangents exterior angles

A

G

B

F

H

O

I

C

E

D

Secants – Tangents & Exterior Angles

Theorem 10.14:If two secants, a secant and a tangent, or two tangents intersect in the exterior of a circle, then the measure of the  formed is ½ the measures of the difference of the intercepted arcs.

mBOC = ½ (m arc BC – m arc HI) mAOC= ½ (m arc AC – m arc AI)mAED= ½ (m arc ABD – m arc AD)


Example 3

Example 3:

Find x.

Theorem 10.14

Multiply each side by 2.

Add x to each side.

Subtract 124 from each side.

Answer: 17


Your turn2

Your Turn:

Find x.

Answer: 111


Example 4

Example 4:

A jeweler wants to craft a pendant with the shape shown. Use the figure to determine the measure of the arc at the bottom of the pendant.

Let x represent the measure of the arc at the bottom of the pendant. Then the arc at the top of the circle will be 360 – x. The measure of the angle marked 40° is equal to one-half the difference of the measure of the two intercepted arcs.


Example 41

Example 4:

Multiply each side by 2 and simplify.

Add 360 to each side.

Divide each side by 2.

Answer: 220


Your turn3

Two sides of a fence to be built around a circular garden in a park are shown. Use the figure to determine the measure of

Your Turn:

Answer: 75


Example 5

Example 5:

Find x.

Multiply each side by 2.

Add 40 to each side.

Divide each side by 6.

Answer: 25


Your turn4

Your Turn:

Find x.

Answer: 9


Assignment

Assignment

  • Pre-AP GeometryPg. 564 #12 - 32

  • Geometry:Pg. 564 #3 – 7, 12 - 26


  • Login