There are 3 parallel chords in a circle. None of them have...

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Question by Timothy
Submitted on 3/5/2004
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There are 3 parallel chords in a circle. None of them have to be the diameter. The top chord has a length of 14, the bottom chord length of 10, and the middle chord a length of a^(1/2). The middle chord is half way between the other chords. The distance between the top and bottom chord is 6. What is the value of a? The answer is suppose to be 184 but I don't know how.

Answer by colin
Submitted on 3/17/2004
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Assume all three chords lie in the same semi-circle. Actually they don't, but this doesn't matter! Draw the obvious diagram. Now add in a radius which bisects all the chords. Let the distance along this radius from the center of the circle to the longest chord be b. So from Pythagoras 7^2+b^2 = r^2, where r is the radius of the circle. Similarly a/4 + (b+3)^2 = r^2 and 5^2 + (b+6)^2 = r^2. That's three equations containing three unknowns, so the rest is simple algebra.

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