Question
In a circle with center O and radius 10 cm, two chords
AB and CD are parallel and 6 cm apart. If the length of chord AB is 16 cm, what is the length of chord CD?Solution
For chord AB, the perpendicular distance from O to AB divides it into two equal halves of 8 cm each. Using Pythagoras in the triangle formed,Ā the perpendicular distance from O to AB = sqrt(10Ā² Ā - 8Ā² )Ā = sqrt(100 - 64) = sqrt(36) = 6 cm. The chords AB and CD are equidistant from the center, so chord CD is also divided into two equal halves. Length of chord CD = 2 * sqrt(10Ā² Ā - 6Ā² )Ā = 2 * sqrt(100 - 36) = 2 * sqrt(64) Ā = 16 cm. Correct answer: b) 16 cm
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