If a chord 24 cm long is 5 cm from the CENTER of a circle, how long is a chord 10 cm from the center?
A chord with length 24 cm at 5 cm from the center GIVES a radius of 13 cm, using a half-length of 12 cm and the distance of 5 cm in Pythagoras’s theorem to find the radius.

Using the same radius and Pythagoras's theorem again, a chord 10 cm from the circle with radius 13 cm has a half-length of sqrt(69), or a full length of double that, so 2*sqrt(69).

Working: If a chord 24 cm long is 5 cm from the center of a circle, how long is a chord 10 cm from the center?
A chord with length 24 cm at 5 cm from the center gives a radius of 13 cm, using a half-length of 12 cm and the distance of 5 cm in Pythagoras’s theorem to find the radius.

Using the same radius and Pythagoras's theorem again, a chord 10 cm from the circle with radius 13 cm has a half-length of sqrt(69), or a full length of double that, so 2*sqrt(69).

Working:


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