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Middle/High School Algebra, Geometry, and Statistics (AGS)
7.15 Theorem 18
Two 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.