1 / 13

10.5 Segment Lengths in Circles

10.5 Segment Lengths in Circles. Objectives/Assignment. Find the lengths of segments of chords. Find the lengths of segments of tangents and secants. Assignment: 2-26 even, 40-54 even. Finding the Lengths of Chords.

lotte
Download Presentation

10.5 Segment Lengths in Circles

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 10.5 Segment Lengths in Circles

  2. Objectives/Assignment • Find the lengths of segments of chords. • Find the lengths of segments of tangents and secants. • Assignment: 2-26 even, 40-54 even

  3. Finding the Lengths of Chords • When two chords intersect in the interior of a circle, each chord is divided into two segments which are called segments of a chord. The following theorem gives a relationship between the lengths of the four segments that are formed.

  4. 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. Theorem 10.15 EA • EB = EC • ED

  5. Chords ST and PQ intersect inside the circle. Find the value of x. RQ • RP =RS •RT Use Theorem 10.15 9 • x = 3 • 6 Substitute values. Simplify. 9x = 18 Divide each side by 9. x = 2 Ex. 1: Finding Segment Lengths

  6. In the figure shown, PS is called a tangent segment because it is tangent to the circle at an end point. Similarly, PR is a secant segment and PQ is the external segment of PR. Using Segments of Tangents and Secants

  7. 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. Theorem 10.16 EA• EB = EC • ED

  8. 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 equal the square of the length of the tangent segment. Theorem 10.17 (EA)2 = EC • ED

  9. Find the value of x. Ex. 2: Finding Segment Lengths RP • RQ = RS • RT Use Theorem 10.16 9•(11 + 9)=10•(x + 10) Substitute values. Simplify. 180 = 10x + 100 Subtract 100 from each side. 80 = 10x Divide each side by 10. 8 = x

  10. Note: • In Lesson 10.1, you learned how to use the Pythagorean Theorem to estimate the radius of a grain silo. Example 3 shows you another way to estimate the radius of a circular object.

  11. Aquarium Tank. You are standing at point C, about 8 feet from a circular aquarium tank. The distance from you to a point of tangency is about 20 feet. Estimate the radius of the tank. Ex. 3: Estimating the radius of a circle

  12. Solution (CB)2 = CE • CD Use Theorem 10.17 (20)28 • (2r + 8) Substitute values. Simplify. 400 16r + 64 Subtract 64 from each side. 336  16r Divide each side by 16. 21  r So, the radius of the tank is about 21 feet.

  13. Ex. 4: Finding Segment Lengths (BA)2 = BC • BD Use Theorem 10.17 (5)2 =x • (x + 4) Substitute values. Simplify. 25 = x2 + 4x Write in standard form. 0 = x2 + 4x - 25 Use Quadratic Formula. x = x = Simplify. Use the positive solution because lengths cannot be negative. So, x = -2 +  3.39.

More Related