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Segment Lengths in Circles

Segment Lengths in Circles. Section 10.5. Essential Questions. How do I find the lengths of segments and chords? How do I find the lengths of segments of tangents and secants?. EA. EB = EC. ED. ×. ×. Chord Product Theorem.

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Segment Lengths in Circles

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  1. Segment Lengths in Circles Section 10.5

  2. Essential Questions • How do I find the lengths of segments and chords? • How do I find the lengths of segments of tangents and secants?

  3. EA EB = EC ED × × Chord Product Theorem • If two chords intersect in the interior of a circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

  4. Let's Investigate This Theorem!

  5. Example 1 • Find the value of x.

  6. Try This! • Find the value of x.

  7. Secant-Secant Theorem • If two secant segments share the same endpoint outside a circle, then the product of the length of one secant segment and the length of its external segment equals the product of the length of the other secant segment and the length of its external segment.

  8. Secant-Tangent Theorem • If a secant segment and a tangent segment share an endpoint outside a circle, then the product of the length of the secant segment and the length of its external segment equals the square of the length of the tangent segment.

  9. Let's Investigate These Theorems!

  10. Example 2 • Find the value of x.

  11. Try This! • Find the value of x.

  12. Example 3 • Find the value of x.

  13. Try This! • Find the value of x.

  14. HOMEWORK • Pages 632-633 • 10 - 27

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