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6.6 Find Segment Lengths in Circles

6.6 Find Segment Lengths in Circles. Vocabulary. Segments of a chord: When two chords intersect in the interior of a circle, each chord is divided into two segments called segments of the chord. TB and BS are segments of chord TS. Vocabulary. Theorem 6.16: Segments of Chords

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6.6 Find Segment Lengths in Circles

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  1. 6.6Find Segment Lengths in Circles

  2. Vocabulary • Segments of a chord: • When two chords intersect in the interior of a circle, each chord is divided into two segments called segments of the chord. TB and BS are segments of chord TS

  3. Vocabulary • Theorem 6.16: Segments of Chords • If two chords intersect in the interior of a circle: EB ED Part 1 Part 1 Part 2 Part 2

  4. Example: • Find the value of x. x * 6 = 5 * 12 6x = 60 x = 10

  5. You Try: • Find ML and JK.

  6. Vocabulary • Secant Segment • A secant segment is a segment that contains a chord of a circle, and has exactly one endpoint outside of the circle. QR is a secant segment

  7. Vocabulary • External Segment • An external segment is the part of a secant segment that is outside the circle. KR is an external segment of the secant segment

  8. Vocabulary • Theorem 6.17: Segments of Secants • If two secant segments share the same endpoint outside of a circle: EB EC WHOLE WHOLE OUTSIDE OUTSIDE

  9. Example: • Find the value of x. RP * RQ = RT * RS (6 + 4) * 6 = (5 + x) * 5 60 = 25 + 5x 35 = 5x 7 = x

  10. You Try: • Find the value of x.

  11. Vocabulary • Theorem 6.18: Segments of Secants and Tangents • If a secant segment and a tangent segment share an endpoint outside a circle: WHOLE OUTSIDE ED EC Tangent2

  12. Example: • Find JK. MJ2 = JL * JK *Use quadratic formula to find x*

  13. a = 1 b = 6 c = -64 Example Cont’d: 0 = x2 + 6x – 64

  14. You Try: • Find RS.

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