10.5 Segment Length in Circles

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10.5 Segment Length in Circles
Geometry 10.5 Segment Length in Circles

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

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

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

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

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

Chords in a Circle Theorem 10.15
Theorem Demo d a b c a  b = c  d Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles

Geometry 10.5 Segment Lengths in Circles
Example 1 Find a. 10  4 = 8  a 40 = 8  a 5 = a 10 5 a 4 8 Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles

Geometry 10.5 Segment Lengths in Circles
Your Turn: Find x. 3x  x = 8  6 3x2 = 48 x2 = 16 x = 4 A D 3x 6 12 E x 4 B 8 C Check: 12  4 = 48 and 8  6 = 48 Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles

Geometry 10.5 Segment Lengths in Circles
Proof 3 and 4 both intercept arc SV. What does this tell use about 3 and 4? They are congruent. What kind of angles are 1 and 2? Vertical Angles And vertical angles are ____. Congruent. R T 3 O 4 1 2 V S Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles

Geometry 10.5 Segment Lengths in Circles
Proof continued Now SOR ~ VOT. Why? AA~ Postulate. In similar triangles, sides are proportional: R T 3 O 4 1 2 V OR  OV = OT  OS S Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles

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

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

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

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

Theorem 10.17 (tangent-secant)
B C D Theorem Demo Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles

Geometry 10.5 Segment Lengths in Circles
Theorem (simplified) c2 = a(a + b) b a c Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles

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

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

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

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

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

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

Geometry 10.5 Segment Lengths in Circles
Solve it. x can’t be negative x  3.39 Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles

Geometry 10.5 Segment Lengths in Circles
All that for just one problem? Just do it! Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles

Geometry 10.5 Segment Lengths in Circles
Your Turn Solve for x. 3 2 x Equation: 32 = x(x + 2) x + 2 Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles

Geometry 10.5 Segment Lengths in Circles
3 2 x Solution 32 = x(x + 2) 9 = x2 + 2x 0 = x2 + 2x – 9 a = 1 b = 2 c = -9 Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles

Theorem 10.16 (secant-secant)
Theorem Demo b a d c a(a+b) = c(c+d) Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles

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

Geometry 10.5 Segment Lengths in Circles
Your Turn Solve for x. 9 11 10 X Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles

Geometry 10.5 Segment Lengths in Circles
Solution 9 11 10 X Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles

Geometry 10.5 Segment Lengths in Circles
Example 4 Solve for x. Equation: 5x = 4(16) Why? 5x = 64 x = 12.8 16 12 5 X 4 Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles

Geometry 10.5 Segment Lengths in Circles
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. Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles

Geometry 10.5 Segment Lengths in Circles
Formula Summary a(a+b) = c(c+d) a b c d c a b c2 = a(a + b) a c d b ab = cd Tuesday, March 24, 2:56 Geometry 10.5 Segment Lengths in Circles

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

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