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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 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.
Assignment p. 732: 8 – 28 (even), 34 p. 740: 7 – 21 odd, 22 Unit Study Guide 9 Quiz - Monday