In a circle, the length of each of two parallel chords is 10. If the distance between these two chords is 24, what is the length of a diameter of this circle?
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MathQuery
ANSWERS: 5
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30
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Pythagorus will tell you the answer. Can you find a right triangle that has a diameter of the circle as the hypotenuse?
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Just draw it out, draw the parallel chords vertically and the distance between them horizontally, then draw a line from the upper right chord/circle intersection to the lower left, and apply Pythagoras's theorem to the triangles thus created. With problems like this, just start with the things you know and draw it out and they become much simpler.
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Thank you Sawdust :) 24^2 + 10^2 = d^2 576 + 100 = d^2 626 = d^2 square root both sides diameter = 26 :D never would have thought to try that :)
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Thanks for this Q. I had fun with it, since I haven't done this kind of thing for ages and ages. Since the two parallel chords are on opposite sides of the diameter (the only way they could be parallel and be the same length) and the distance between them is therefore half on one side of the circle and half on the other, then we know two sides of a right triangle inscribed in the circle: One side is 12 (half of the distance between the chords) and one side is 5 (half of the chord length). So we have a triangle with sides 12, 5 and r, where r is the hypotenuse of the triangle AND the radius of the circle. (The hypotenuse is formed from the midpoint of the line segment that spans the distance between the chords at their midpoints, running through the center of the circle, and runs to the end of any one of the chords with length 10. Applying the formula to determine the length of the hypotenuse of a right triangle: a^2 + b^2 = c^2 and substituting: 5^2 + 12^2 = r^2 25 + 144 = 169 = 13^2 So the radius is 13 and the diameter is twice that, or 26.
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