Secants tangents and angle measures special segments in a circle
Download
1 / 24

Secants, Tangents, and Angle Measures Special Segments in a Circle - PowerPoint PPT Presentation


  • 235 Views
  • Uploaded on

Secants, Tangents, and Angle Measures Special Segments in a Circle. Notes 28 – Sections 10.6 & 10.7. Essential Learnings. Students will understand and be able to find measures of segments that intersect in the interior of a circle.

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

PowerPoint Slideshow about ' Secants, Tangents, and Angle Measures Special Segments in a Circle' - gretchen-torres


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
Secants tangents and angle measures special segments in a circle

Secants, Tangents, and Angle MeasuresSpecial Segments in a Circle

Notes 28 – Sections 10.6 & 10.7


Essential learnings
Essential Learnings

  • Students will understand and be able to find measures of segments that intersect in the interior of a circle.

  • Students will understand and be able to find measures of segments that intersect in the exterior of a circle.

  • Students will understand and be able to find measures of angles formed by lines intersecting on or inside a circle.

  • Students will be able to find measures of angles formed by lines outside a circle.


Vocabulary
Vocabulary

  • Secant – a line that intersects a circle in exactly two points.


Theorem 10 12
Theorem 10.12

  • If two secants or chords intersect in the interior of a circle, then the measure of an angle formed is one half the sum of the measure arcs intercepted by the angle and its vertical angle.


Example 1
Example 1

Find x.


Example 2
Example 2

Find the measure of arc TS.


Theorem 10 13
Theorem 10.13

  • If a secant and a tangent intersect at the point of tangency, then the measure of each angle formed is one half the measure of its intercepted arc.


Example 3
Example 3

Find the measure of ∠TRQ.


Example 4
Example 4

Find the measure of arc BD.


Theorem 10 14
Theorem 10.14

  • If two secants, a secant and a tangent, or two tangents intersect in the exterior of the circle, then the measure of the angle formed is one half the difference of the measures of the intercepted arcs.


Theorem 10 141
Theorem 10.14

  • If two secants intersect:


Theorem 10 142
Theorem 10.14

  • If a secant and a tangent intersect:


Theorem 10 143
Theorem 10.14

  • If two tangents intersect:


Example 5
Example 5

Find the measure of arc GJ.


Example 6
Example 6

Find the measure of ∠T.


Segments of chords theorem
Segments of Chords Theorem

  • If two chords intersect in a circle, then

    ABBC = EBBD


Example 11
Example 1

Find x.


Secant segments theorem
Secant Segments Theorem

  • If two secants intersect in the exterior of a circle, then

    AB AC= AD  AE


Example 21
Example 2

  • Find x.


Quadratic formula
Quadratic Formula

  • Given a quadratic equation in standard form:

  • To solve, either factor or use Quadratic Formula.

    The Quadratic Formula:


Tangent secant theorem
Tangent-Secant Theorem

  • If a tangent and a secant intersect in the exterior of a circle, then

    JK2 = JLJM


Example 31
Example 3

LM is tangent to the circle. Find x.


Example 3 using quad form
Example 3 – Using Quad. Form.

LM is tangent to the circle. Find x.


Assignment
Assignment

p. 732: 8 – 28 (even), 34

p. 740: 7 – 21 odd, 22

Unit Study Guide 9

Quiz - Monday


ad