SOLUTION: Two concentric circles are shown. The radius of the inner circle is 3, and the distance between the circles is 3. A line segment of length 4 has its endpoints on both circles. Comp

Algebra ->  Surface-area -> SOLUTION: Two concentric circles are shown. The radius of the inner circle is 3, and the distance between the circles is 3. A line segment of length 4 has its endpoints on both circles. Comp      Log On


   



Question 1071413: Two concentric circles are shown. The radius of the inner circle is 3, and the distance between the circles is 3. A line segment of length 4 has its endpoints on both circles. Compute the distance from point A to point B.
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Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Assume that the center of the circles is the origin (0,0),
The outer circle is,
x%5E2%2By%5E2=6%5E2
1.x%5E2%2By%5E2=36
If we make a circle centered at the intersection of the 3 and 4 lines with a radius of 4, it would be,
x%5E2%2B%28y-3%29%5E2=4%5E2
2.x%5E2%2B%28y%2B3%29%5E2=16
We can find the intersection of the outer circle and the new circle,
From 1,
x%5E2=36-y%5E2
Substituting into 2,
36-y%5E2%2B%28y%2B3%29%5E2=16
36-y%5E2%2By%5E2%2B6y%2B9=16
6y%2B45=16
6y=-29
y=-29%2F6
So then,
x%5E2%2B%28-29%2F6%29%5E2=36
x%5E2=36-%28-29%2F6%29%5E2
x%5E2=1296%2F36-841%2F36
x%5E2=455%2F36
x=-sqrt%28455%29%2F6
So now find the distance between (0,-6) and (-sqrt%28455%29%2F6,-29%2F6).
D%5E2=%28-sqrt%28455%29%2F6-0%29%5E2%2B%28-29%2F6-%28-6%29%29%5E2
D%5E2=455%2F36%2B%28-29%2F6%2B36%2F6%29%5E2
D%5E2=455%2F36%2B%287%2F6%29%5E2
D%5E2=455%2F36%2B49%2F36
D%5E2=504%2F36
D%5E2=14
D=sqrt%2814%29
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