SOLUTION: A chord of a circle is 32 meters long and it is 30 meters from the center of the circle. find the diameter of the circle

Algebra ->  Circles -> SOLUTION: A chord of a circle is 32 meters long and it is 30 meters from the center of the circle. find the diameter of the circle       Log On


   

Question 755754: A chord of a circle is 32 meters long and it is 30 meters from the center of the circle. find the diameter of the circle
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A chord of a circle is 32 meters long and it is 30 meters from the center of the circle. find the diameter of the circle
----------------
(r+30)*(2r-30) = 256
r%5E2+%2B+15r+-+578+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B15x%2B-578+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2815%29%5E2-4%2A1%2A-578=2537.

Discriminant d=2537 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-15%2B-sqrt%28+2537+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2815%29%2Bsqrt%28+2537+%29%29%2F2%5C1+=+17.6843205189261
x%5B2%5D+=+%28-%2815%29-sqrt%28+2537+%29%29%2F2%5C1+=+-32.6843205189261

Quadratic expression 1x%5E2%2B15x%2B-578 can be factored:
1x%5E2%2B15x%2B-578+=+%28x-17.6843205189261%29%2A%28x--32.6843205189261%29
Again, the answer is: 17.6843205189261, -32.6843205189261. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B15%2Ax%2B-578+%29

===============
r = 17.6843
d = 35.3686 meters