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Geometry 10.5 Segment Length in Circles

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Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles2 Goals Find the lengths of segments of chords. Find the lengths of segments and tangents. 2-Day Lesson

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Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles3 Quadratic Equation Review A quadratic equation is in the form Any quadratic equation can be solved using the formula Skip

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Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles4 Solve:

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Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles5 Solve:

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Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles Chords in a Circle

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Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles7 Chords in a Circle Theorem a c d b a b = c d Theorem Demo

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Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles8 Example 1Find a = 8 a 40 = 8 a 5 = a 5 a

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Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles9 Your Turn:Find x. A B C D E 3x x 8 3x x = 8 6 3x 2 = 48 x 2 = 16 x = Check: 12 4 = 48 and 8 6 = 48

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Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles10 Proof R S O T V and 4 both intercept arc SV. What does this tell use about 3 and 4? They are congruent. What kind of angles are1 and 2? Vertical Angles And vertical angles are ____. Congruent.

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Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles11 Proof continued R S O T V Now SOR ~ VOT. Why? AA~ Postulate. In similar triangles, sides are proportional: OR OV = OT OS

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Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles12 Terminology This line is a secant. This segment is a secant segment.

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Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles13 Terminology This segment is the external secant segment.

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Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles14 Terminology This line is a tangent. This segment is a tangent segment.

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Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles15 Terminology A B C D AC is a __________________. AB is the _________________________. AD is a _________________. external secant segment secant segment tangent segment

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Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles16 Theorem (tangent-secant) A B C D Theorem Demo

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Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles17 Theorem (simplified) a b c c 2 = a(a + b)

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Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles18 Example 2Find AD. A B C D 6 4

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Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles19 Your Turn.Solve for x. x 4 4 8

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Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles20 Turn it up a notch… x 5 4 Now What?

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Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles21 Quadratic Equation Set quadratic equations equal to zero.

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Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles22 Quadratic Formula 1 a = 1 b = 4 c = -25

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Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles23 Quadratic Formula 1 a = 1 b = 4 c = -25

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Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles24 Solve it. x cant be negative x 3.39

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Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles25 Just do it!

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Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles26 Your TurnSolve for x. Equation: 3 2 = x(x + 2) 3 2 x x + 2

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Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles27 Solution 3 2 x 3 2 = x(x + 2) 9 = x 2 + 2x 0 = x 2 + 2x – 9 a = 1 b = 2 c = -9

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Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles28 Theorem (secant-secant) a b c d a(a+b) = c(c+d) Theorem Demo

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Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles29 Example 3Solve for x X Solution: 5(5 + 8) = 6(6 + x) 5(13) = x 65 = x 29 = 6x x = 4 5/6 (or 4.83)

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Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles30 Your TurnSolve for x X

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Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles31 Solution X

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Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles32 Example 4Solve for x X Equation: 5x = 4(16) Why? 5x = 64 x =

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Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles33 Summary Segments in a circle have three situations: Chord-Chord Secant-Tangent Secant-Secant Do you know the formula for each? Read the problems carefully. Use the correct numbers for each variable.

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Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles34 Formula Summary c a b c 2 = a(a + b) a c d b a b = c d a(a+b) = c(c+d) a b c d

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Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles35 Homework

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