SOLUTION: in a circle of radius 20 cm the distance between a pair of equal and parallel chords is 24 cm find how long the chords are

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Question 453456: in a circle of radius 20 cm the distance between a pair of equal and parallel chords is 24 cm find how long the chords are
Answer by pedjajov(51) About Me  (Show Source):
You can put this solution on YOUR website!
If we join center of the circle with the ends of the chord we are getting two isosceles triangles with base equal to the length of the chord and legs equal to the radius of the circle.
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Next if we draw a line that is perpendicular on both chords and goes thru the center of the circle it makes a distance between these two chords. Segment that goes from center of the circle to one of the chords is half of that distance, 12cm. That segment halves the chord.
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Now we have a right triangle with:
- one leg equal to the half of the distance, 24/2=12cm
- one leg equal to the half of the chord length, l/2
- hypotenuse equal to the radius of the circle, 20cm
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We'll use Pythagorean theorem to find the length of the second leg:
12%5E2%2B%28l%2F2%29%5E2=20%5E2
144%2Bl%5E2%2F4=400, multiply by 4
576%2Bl%5E2=1600, subtract 576
l%5E2=1024, take a square root of both sides
l=32
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Length of each chord is 32cm.