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Bellwork

Clickers. Bellwork. If 10 is multiplied by 10 more than a number, the product is the square of 24. Find the number Solve for x 21(x-4)=(2x-7)(x+2) 3x 2 -13x-7=0. Bellwork Solutions. If 10 is multiplied by 10 more than a number, the product is the square of 24. Find the number.

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Bellwork

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  1. Clickers Bellwork • If 10 is multiplied by 10 more than a number, the product is the square of 24. Find the number • Solve for x • 21(x-4)=(2x-7)(x+2) • 3x2-13x-7=0

  2. Bellwork Solutions • If 10 is multiplied by 10 more than a number, the product is the square of 24. Find the number

  3. Bellwork Solutions • Solve for x • 21(x-4)=(2x-7)(x+2) • 3x2-13x-7=0

  4. Section 10.6 Find Segment Lengths in Circles

  5. The Concept • After discussing most of the angle relationships that we can find in a circle, today we’re going to move on to chord lengths • The concepts that drive our theorems today are based on the relationships we’ve already seen within a circle, but just need to be defined

  6. Definition Segments of a chord The line segments formed when a chord is divided into two or more pieces Secant Segment Segment that contains a chord of a circle and has exactly one endpoint outside the circle. External Segment Exterior portion of secant segment C H G F E D A B

  7. Theorem Theorem 10.14 If two chords intersect in the interior of a circle, then the product of the lengths of the segment of one chord is equal to the product of the lengths of the segments of the other chord. C A E D B

  8. Example Solve for x A C x+1 x+5 3 E B x+3 D

  9. On your own • Solve for x A D x 8 x+8 6 C B

  10. On your own • Solve for x A D x x x+10 14 C B

  11. Theorem Theorem 10.15 If two secant segments share the same endpoint outside a circle, then the product of the lengths of one secant segment and its external segment equals the product of the lengths of the other secant segment and its external segment D A E C B

  12. Example Solve for x 3 4 A C 5 x E B D

  13. On your own • Solve for x A 3 4 E x 2 C B

  14. Theorems Theorem 10.16 If a secant segment and a tangent segment share an endpoint outside a circle, then the product of the lengths of the secant segment and its external segment equals the square of the length of the tangent segment A D C B

  15. Example Find the measure of angle AEC 16 x 8

  16. On your own • What is the measure of angle ABC 15 x 14

  17. Homework • 10.6 • 1, 2-22 even

  18. Most Important Points • Segment Length formulas for inside a circle

  19. On your own • What is the measure of angle of E, if arc ABC is 200o A D B C E

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