Warm up
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Warm up. 2 – 18 evens only. This will be graded in 10 minutes. 2.79 27.93 61.78 138.4 7.16 309.4 ° 107 ° 16.1.6 ° 18.72.5 °. 9.2 Tangents and Secants. Tangents and secants are LINES. A tangent line intersects the circle at exactly ONE point.

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Warm up

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Warm up

Warm up

  • 2 – 18 evens only.

  • This will be graded in 10 minutes.

  • 2.79

  • 27.93

  • 61.78

  • 138.4

  • 7.16

  • 309.4°

  • 107 °

  • 16.1.6 °

  • 18.72.5 °


9 2 tangents and secants

9.2 Tangents and Secants

Tangents and secants are LINES.

A tangent line intersects the circle at exactly ONE point.

A secant line intersects the circle at exactly TWO points.


A little extra information

A little extra information

  • The word tangent comes from the Latin word meaning to touch

  • The word secant comes from the Latin word meaning to cut.


Important theorems

Important Theorems

  • Tangent Theorem:

    • If a line is tangent to a circle, then the line is perpendicular to a radius of the circle drawn to the point of tangency.

The line AB is tangent to circle C at B.

How could we prove that segment CB and line AB are perpendicular?


Converse of the tangent theorem

Converse of the Tangent Theorem

  • Go waaaayyy back… how do we get a converse statement?

  • What would be the Converse of the Tangent Theorem?

  • If a line is perpendicular to a radius of a circle at its endpoint on the circle, then the line is tangent to the circle.


Radius and chord theorem

Radius and Chord Theorem

  • A radius that is perpendicular to the chord of a circle bisects the chord.

QR = 3

What is the measure of RS?

XR = 7 and WR = 2

Find the missing measures of the remaining segments.

RZ =

RY =

XW =

WZ =

XZ =

7

7

6.7

6.7

13.4


Let s practice

Let’s Practice

I need 2 volunteers to hand out whiteboards and markers.


Your assignment

Your assignment

  • Pg 577; 10-13, 19-26

  • Pg 846, Lesson 9.2, 1-6


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