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Question 166477: The radius of a circle is 5 and its center is at (-3,-4). Find the lenght of the chord that is bisected at (-11/12, -13/12).
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! First, find the distance between the center and the bisected point is:
Do this using the "distance formula" between two points:
d = sqrt[(x2-x1)^2 + (y2-y1)^2]
(-3,-4) and (-11/12, -13/12)
d = sqrt[(-11/12+3)^2 + (-13/12+4)^2]
d = sqrt[(-11/12+36/12)^2 + (-13/12+48/12)^2]
d = sqrt[(25/12)^2 + (35/12)^2]
d = sqrt[4.34 + 8.51]
d = sqrt[12.85]
d = 3.584
.
Drawing a diagram of the problem will help you see that the "distance between the center and bisector", "half the chord" and the "radius" forms a right triangle -- allowing you to apply the pythagorean theorem:
Let x = half the length of the chord
then
x^2 + 3.584^2 = 5^2
x^2 + 12.847 = 25
x^2 = 12.153
x = 3.486
.
Length of chord is
2x = 2(3.486) = 6.972
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