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Arik Amin

Arik Amin. Congruent Chords Section 10.2. Definitions. Radius – A segment joining the center of a circle to a point on the circle. Examples: OX,OY,OA, & OB (also hypotenuses) Chord – A segment joining two points on a circle. Examples: XY, AB, AY & BX. Definitions.

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Arik Amin

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  1. Arik Amin Congruent Chords Section 10.2

  2. Definitions • Radius – A segment joining the center of a circle to a point on the circle. • Examples: OX,OY,OA, & OB (also hypotenuses) • Chord – A segment joining two points on a circle. • Examples: XY, AB, AY & BX

  3. Definitions • The longest chord of a circle is the diameter. • Diameter – A chord that passes through the center of a circle. • Examples: BX & AY (They are also chords)

  4. What’s OM & ON? • OM & ON are one of the two legs of the right triangle. • The distance from the center of a circle to a chord is the length of the segment from the center to the chord. • OM is the distance from O to chord AB. • ON is the distance from O to chord XY.

  5. Theorem 77 & 78 • If two chords of a circle are equidistant from the center, then they are congruent. • If two chords of a circle are congruent, then they are equidistant from the center of the circle. (Converse)

  6. Circle O is the center, OM AB, ON XY, OM ON Draw OA,OB,OX,OY OA OB OX OY AOB XOY AOB XOY AB XY Given 2 points determine a segment All radii of a circle are Vertical s are SAS (3,3,4) CPCTC Proving the Theorem

  7. Given: Circle O is the center, OM ON XY= 6x + 14 AB= 4 – 4x FIND: XY SOLUTION: Since OM ON, XY AB 6x + 14 = 4 – 4x 10x = -10 x = -1 XY = 8 Sample Problem

  8. Sample Problem • Given: Center of the circle is O, OD AB, OE CB, OD OE • Prove: A C

  9. Center of the circle is O, OD AB, OE CB, OD OE 2. AB BC 3. A C Given. If two chords of a circle are equidistant from the center, then they are congruent. If sides then angles. Sample Problem Answer

  10. Exercises • Pages 447-449 • 1. Same distance • 6a. 8cm b. Circle • 7a. 283.53 sq mm 7b. 59.69mm • 11a. 8 • 11b. 5 • 13. 10 • 15a. 8 • 15b. 24+6 7

  11. Works Citied George Milauskas, Richard Rhoad, & Robert Whipple. GEOMETRY for enjoyment and Challenge. US, 1991. “Math Warehouse”. Congruent Chords of circles. 296 may 2008. http://www.mathwarehouse.com/geometry/circle/chord-equidistant-from-center.htm More problems are at the website.

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