SOLUTION: I just want to check if my answer is correct.
Problem: The center of the circle is at (-3,-2). If a chord of length 4 is bisected at (3,1), find the length of the radius.
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Problem: The center of the circle is at (-3,-2). If a chord of length 4 is bisected at (3,1), find the length of the radius.
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Question 924004: I just want to check if my answer is correct.
Problem: The center of the circle is at (-3,-2). If a chord of length 4 is bisected at (3,1), find the length of the radius.
My answer is: 3√6 Answer by Theo(13342) (Show Source):
so you get a triangle formed by the radius of the circle and the chord such that the ends of the chord that connect to the center of the circle are each a radius of the circle.
the chord is 4 units in length.
two right triangles are formed with each right triangle having a base of 2 which is 1/2 the length of the chord.
the length of the line segment formed by the radius that bisects the chord is found by taking the 2 points common to that radius and finding the distance between them.
the two points are (-3,-2) and (3,1)
the distance between them will be square root of [(-2-1)^2 + (-3-3)^2] which becomes square root of [9 + 36] which becomes square root of (45).
your right triangle has one leg of 2 and one leg of sqrt(45)
to find the hypotenuse of the right triangle which is the radius of the circle, you need to use the pythagorean formula.
you will get r^2 = 2^2 + sqrt(45)^2
that becomes r^2 = 4 + 45 which makes r^2 = 49 which makes r = 7.
the radius of your circle has to be 7.
the equation of your circle becomes:
(x+3)^2 + (y + 2)^2 = 49
a graph of the circle and the chord and the radius that bisects the chord is shown below:
all the numbers check out.
the radius is 7
each sice of the chord that is bisected by the radius has a length of 2.
