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10-7 ~ Segments of Tangents, Secants, & Chords

10-7 ~ Segments of Tangents, Secants, & Chords. Segment Relationships. External Secant Segment. Secant Segment. Tangent Segment. Relationships. 2 Tangents If two tangent segments intersect at the same point, then the two tangent segments are congruent Tangent = Tangent. Practice.

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10-7 ~ Segments of Tangents, Secants, & Chords

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  1. 10-7 ~ Segments of Tangents, Secants, & Chords

  2. Segment Relationships External Secant Segment Secant Segment Tangent Segment

  3. Relationships • 2 Tangents • If two tangent segments intersect at the same point, then the two tangent segments are congruent • Tangent = Tangent

  4. Practice 16,000 mi N

  5. Solution • Tangent = Tangent N = 16,000 mi

  6. Relationships • 2 Secants • Product of the lengths of the secant segment and external secant segment is equal for both secants • Whole • Outside = Whole • Outside

  7. Practice 60 m 50 m 55 m Y

  8. Solution • Whole • Outside = Whole • Outside 110 m • 50 m = (Y + 55) • 55 m 5500 m = 55Y + 3025 2475 m = 55Y Y = 45 m

  9. Relationships • Secant & Tangent • If a secant and a tangent intersect outside a circle then the product of the lengths of the secant segment and the external segment is equal to the tangent segment squared. • Whole • Outside = Tangent2

  10. Practice 6 mi 4 mi P

  11. Solution Whole • Outside = Tangent2 (P + 4)• 4 mi = (6 mi)² 4P + 16 = 36 mi 4P = 20 P = 5 mi

  12. Relationships • 2 Chords • If two chords intersect inside a circle, then the product of the lengths of the segments of one chord equals the product of the lengths of the segments of the other chord • top • bottom = Left • Right t R L b

  13. Practice 5 cm X 4 cm 3 cm

  14. Solution Top • Bottom = Left • Right 5 cm • 3 cm = 4 cm • X X = 3.75 cm

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