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### Middle/High School Algebra, Geometry, and Statistics (AGS)7.15 Theorem 18Two Chords are equal in a Circle

 Example: In the above figure if the radius of the circle is 26 and the distance of the chord from the center to the midpoint of the chord is 10. Find the length of the the chord. Given: Radius of the circle is 26 that is OA = OC = 26 OL = OM = 10 OLA and OMC are two right triangles. Using pythagorean theorem: OA2 = AL2 + OL2 262 = AL2 + 102 676 = AL2 + 100 AL2 = 676 - 100 AL2 = 576 AL = 24 Therefore the length of the chord AB is 2 x AL = 48. Directions: Write at least two examples of your own.

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