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Find the lengths of segments formed by lines that intersect circles.

Objectives. Find the lengths of segments formed by lines that intersect circles. Use the lengths of segments in circles to solve problems. J. Example 1: Applying the Chord-Chord Product Theorem. Find the value of x. 10(7) = 14 ( x ). 70 = 14 x. 5 = x. EF = 10 + 7 = 17.

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Find the lengths of segments formed by lines that intersect circles.

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  1. Objectives Find the lengths of segments formed by lines that intersect circles. Use the lengths of segments in circles to solve problems.

  2. J Example 1: Applying the Chord-Chord Product Theorem Find the value of x. 10(7) = 14(x) 70 = 14x 5 = x EF = 10 + 7 = 17 GH = 14 + 5 = 19

  3. Check It Out! Example 1 Find the value of x and the length of each chord. 8(x) = 6(5) 8x = 30 x = 3.75 AB = 6 + 5 = 11 CD = 3.75 + 8 = 11.75

  4. 6 in. Check It Out! Example 2 Suppose the length of chord AB that the archeologists measured was 12 in. Find QR. 6(6) = 3(QR) 12 = QR 12 + 3 = 15 = PR

  5. Example 3: Applying the Secant-Secant Product Theorem Find the value of x and the length of each secant segment. 112 = 64 + 8x 48 = 8x 6 = x ED = 7 + 9 = 16 EG = 8 + 6 = 14

  6. Check It Out! Example 3 Find the value of z and the length of each secant segment. 351 = 169 + 13z 182 = 13z 14 = z LG = 30 + 9 = 39 JG = 14 + 13 = 27

  7. Example 4: Applying the Secant-Tangent Product Theorem Find the value of x. ML JL = KL2 20(5) = x2 100 = x2 ±10 = x The value of x must be 10 since it represents a length.

  8. Check It Out! Example 4 Find the value of y. DE DF = DG2 7(7 + y) = 102 49 + 7y = 100 7y = 51

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