Suppose a chord is 20 inches long and is 24 inches from the center of the circle. How do you find the length of the radius?

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Suppose a chord is 20 inches long and is 24 inches from the center of the circle. How do you find the length of the radius?

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Answer 1 · 2016-03-10T17:02:25

$r = 26$ $r = 26"$

Explanation:

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A line segment from the 20" chord to the center of the circle is a perpendicular bisector of the chord creating a right triangle with legs of 10" and 24" with radius of the circle forming the hypotenuse.

We can use the Pythagorean theorem to solve for the radius.

$a^{2} + b^{2} = c^{2}$ $a^2 + b^2 = c^2$

a = 10"
b = 24"
c = ?"

$10^{2} + 24^{2} = r^{2}$ $10^2 + 24^2 = r^2$
$100 + 576 = r^{2}$ $100 + 576 = r^2$
$676 = r^{2}$ $676 = r^2$
$\sqrt{676} = r$ $sqrt676 = r$
$26 = r$ $26" = r$

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Suppose a chord is 20 inches long and is 24 inches from the center of the circle. How do you find the length of the radius?

1 Answer

Explanation:

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