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Secants, Tangents, and Angle Measures Special Segments in a CirclePowerPoint Presentation

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

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### 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
ABBC = EBBD

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 = JLJM

Example 3

LM is tangent to the circle. Find x.

Example 3 – Using Quad. Form.

LM is tangent to the circle. Find x.

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