1 / 9

Properties of Chords and Arcs

Properties of Chords and Arcs. Part 1. Definition of Chord. A chord is a segment that has its endpoints on a circle. An arc is part of a circle. P. Q. 6. r. 4. T. r. S. Review Example. PQ is tangent to circle S at P. Find the length of a radius r. Use the Pythagorean Theorem!.

kimberly
Download Presentation

Properties of Chords and Arcs

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. Properties of Chords and Arcs Part 1

  2. Definition of Chord • A chord is a segment that has its endpoints on a circle. • An arc is part of a circle.

  3. P Q 6 r 4 T r S Review Example PQ is tangent to circle S at P. Find the length of a radius r. Use the Pythagorean Theorem! PS2 + PQ2 = SQ2 r2 + 62 = (r + 4)2 r2 + 36 = r2 + 8r + 16 36 = 8r + 16 20 = 8r r = 20/8 = 2.5

  4. E B 30 in C 8 in 14 in D A Example 2 A belt fits around two pulleys. Find the distance between the pulleys. AE2 + ED2 = AD2 (14-8)2 + 302 = AD2 62 + 302 = AD2 AD2 = 936 AD = 30.6 in

  5. P Q 15 in r 9 in T r O Example 3 PQ is tangent to circle O at P. Find the length of a radius r. PO2 + PQ2 = OQ2 r2 + 152 = (r + 9)2 r2 + 225 = r2 + 18r + 81 225 = 18r + 81 144 = 18r r = 144/18 = 8 in

  6. Example 4 Is LM tangent to circle N at L? L M 24 If LM is tangent to circle N, then LMN is a right triangle. 25 N 72 + 242 = 49 + 576 = 625 625 = 252 Therefore, LMN is a right triangle

  7. Circumscribing Circles The sides of the triangle are tangent to the circle. The triangle is circumscribed about the circle. The circle is inscribed in the triangle.

  8. Theorem 12-4: If AB and CB are tangent to circle Ο at A and C, then AB  CB Circumscribing Circles A O B C

  9. A 10 cm D 15 cm F O B 8 cm E C Example 5 Circle O is inscribed in ABC. Find the perimeter of ABC. AD = AF = 10 cm BD = BE = 15 cm CF = CE = 8 cm The perimeter is AD + AF + BD + BE + CF + CE perimeter = 10 + 10 + 15 + 15 + 8 + 8 = 66 cm

More Related