Secants tangents and angle measures special segments in a circle
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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.

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

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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


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