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Ok so I have to put (1,7) into that equation you gave me??

Here is another way of solving.

Here is a circle with two points on it and a chord drawn through them.
|dw:1435785536910:dw|

|dw:1435785591709:dw|

You are given three points on the circle.
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Use a chord again and a perpendicular bisector again:
|dw:1435785724236:dw|

Ok so how can I figure out the equation by using that method?

Where the perpendicular bisectors of the chords intersect is the center of the circle.

Ok. Let's start.
|dw:1435785943459:dw|

|dw:1435786061026:dw|

|dw:1435786091850:dw|

Ok

1. Find the slope of the segment
\(m = \dfrac{6 - 7}{8 - 1} = \dfrac{-1}{7} = -\dfrac{1}{7} \)

The slope of the perpendicular bisector is m = 7

ok

Ok

We have a point and the slope, so we can find the equation of that perpendicular bisector.

Now we need to choose another set of two points on the circle and do the same.

Ok so how would I plug that in this equation?
x^2 + y^2__x__y=0

|dw:1435786849703:dw|

|dw:1435786887498:dw|

Now we have the chord in black in the last figure above.
We need its slope and its midpoint.

ok

ok

Ok

|dw:1435787686770:dw|

All we need now the to find the radius, so we can find r in the equation of the circle.

Ok

Ok

ok

So it would be 5 right?

Ok

|dw:1435788411933:dw|

Thank you!

You're welcome.