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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 Measures Special Segments in a Circle

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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

- 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.

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

- 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.

Find x.

Find the measure of arc TS.

- 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.

Find the measure of ∠TRQ.

Find the measure of arc BD.

- 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.

- If two secants intersect:

- If a secant and a tangent intersect:

- If two tangents intersect:

Find the measure of arc GJ.

Find the measure of ∠T.

- If two chords intersect in a circle, then
ABBC = EBBD

Find x.

- If two secants intersect in the exterior of a circle, then
AB AC= AD AE

- Find x.

- Given a quadratic equation in standard form:
- To solve, either factor or use Quadratic Formula.
The Quadratic Formula:

- If a tangent and a secant intersect in the exterior of a circle, then
JK2 = JLJM

LM is tangent to the circle. Find x.

LM is tangent to the circle. Find x.

p. 732: 8 – 28 (even), 34

p. 740: 7 – 21 odd, 22

Unit Study Guide 9

Quiz - Monday