Shortest Distance

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(Maud, better jump in early).

A semicircle has a radius of r centimeters. A chord (not the diameter) is parallel to the diameter.
If the length of the chord is 2/3 the length of the diameter, what is the shortest distance from the chord to the diameter in terms of r?

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If the length of the chord is 2/3 the length of the diameter, what is the shortest distance from the chord to the diameter in terms of r?

The same as the maximum distance from the chord to the diameter in terms of r!

Cheers,
Paul Edstein
[Fmr MS MVP - Word]

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The line segment from the midpoint of the diameter to the midpoint of the chord forms one leg of a right triangle whose other leg goes from the midpoint of the chord to one end of the chord and whose hypotenuse is r centimeters. I believe that the length of the former leg would be the square root of (r**2 – (2/3r)**2), or r/3 times the square root of 5, centimeters.

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Perfect, DavidHLevin

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