Secants tangents and angle measures special segments in a circle
This presentation is the property of its rightful owner.
Sponsored Links
1 / 24

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


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

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.

Download Presentation

Secants, Tangents, and Angle Measures Special Segments in a Circle

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 MeasuresSpecial 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.

  • 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

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


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

Find x.


Example 2

Find the measure of arc TS.


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

Find the measure of ∠TRQ.


Example 4

Find the measure of arc BD.


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 10.14

  • If two secants intersect:


Theorem 10.14

  • If a secant and a tangent intersect:


Theorem 10.14

  • If two tangents intersect:


Example 5

Find the measure of arc GJ.


Example 6

Find the measure of ∠T.


Segments of Chords Theorem

  • If two chords intersect in a circle, then

    ABBC = EBBD


Example 1

Find x.


Secant Segments Theorem

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

    AB AC= AD  AE


Example 2

  • Find x.


Quadratic Formula

  • Given a quadratic equation in standard form:

  • To solve, either factor or use Quadratic Formula.

    The Quadratic Formula:


Tangent-Secant Theorem

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

    JK2 = JLJM


Example 3

LM is tangent to the circle. Find x.


Example 3 – Using Quad. Form.

LM is tangent to the circle. Find x.


Assignment

p. 732: 8 – 28 (even), 34

p. 740: 7 – 21 odd, 22

Unit Study Guide 9

Quiz - Monday


  • Login