1 / 11

Geometry

Learn the Circle Intersection Theorem, External Point Secants Theorem, and External Point Tangents Theorem with examples and solutions.

sumrall
Download Presentation

Geometry

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. Geometry 9.7 Circles and Lengths of Segments

  2. Q S X R P Theorem • When two chords intersect inside a circle, the product of the segments of one chord equals the product of the segments of the other chord. 4 3 x 8 6 8 x 3 = 6 x 4

  3. D A B P C Example Another way to solve would be to think of two numbers that multiply to 36 and add to 15. b. If AP = 4, PB = 9, and CD = 15, find CP. x 4 P 9 15 - x 9 x 4 = x(15 – x) 36 = 15x – x2 x2 – 15x + 36 = 0 - - (x )(x ) = 0 3 12 CP is either 12 or 3. x – 3 = 0 or x – 12 = 0 If it were given that the figure was drawn to scale, then CP = 12. x = 3 or x = 12

  4. E D F G H Theorem • When two secant segments are drawn to a circle from an external point, the product of one secant segment and its external segmentequalsthe product of the other secant segment and its external segment. FD x FE = FH x FG External x Whole Thing = External x Whole Thing

  5. P P S S T T Q Q R R Example a. If PQ = 9, QR = 3, and TR = 4, then SR = ____. b. If PQ = 11, SR = 12, and TR = 5, find PR. 9 3(12) = 4x 12 36 = 4x x PR = x + 11 = (4) + 11 = 15 4 9 = x 3 RS = 9 x(x + 11) = 5(12) x2 + 11x = 60 x2 + 11x – 60 = 0 11 x + 11 - + (x )(x ) = 0 4 15 12 5 x x – 4 = 0 or x + 15 = 0 x = 4 or x = -15 x must be positive

  6. A P B C Theorem • When a secant segment and a tangent segment are drawn to a circle from an external point, the product of the secant segment and its external segment is equal to the square of the tangent segment. PB x PC = (PA)2 External x Whole Thing = (Tangent)2

  7. T T S S R R Q Q Example 25 5 a. If RT = 25 and RS = 5, find QR. b. IF QR = 6 and ST = 9, find RS. x x2 = 5(25) x2 = 125 x= 5√5 x + 9 QR= 5√5 9 x x(x + 9) = 62 x2 + 9x = 36 x must be positive. x2 + 9x – 36 = 0 6 (x )(x ) = 0 - + 3 12 x – 3 = 0 or x + 12 = 0 RS = 3 x = 3 or x = -12

  8. R U T Q S • Complete. • If RQ=8, QS = 6, and TQ = 16, then QU = ____. • 2. If RS =13, RQ = 7, and QU = 3, then TQ = ____. • 3. If TU = 10√2, QU = 2√2 , and RQ = 8, then RS ____. • 4. If RS = 17, TQ = 18, and QU = 4, then RQ = ___. 3 14 Q 12 8 or 9 Who can fill in the picture on the front board?

  9. D E F G H Complete. 5. If DF = 17, EF = 3, and GF = 6, then HF = ____. 6. If HG = 8, GF = 7, and DF = 21, then EF = ____. 7. If GF = 8, HG = 10, and DE = 18, then EF = ____. 8. If DF = 25, EF = 4, and HG = GF = x, then x = ____. 8.5 5 6 5√2

  10. 15 x 4 5 8 12 16 x x 3x x Secants and tangents are shown. Find the value of x. 9) 10) 11) 12) x = 6 x = 3 x = 9 x = 4

  11. HW • pg. 364 #1-9, 13-20

More Related