SOLUTION: A square OABC is drawn with vertices as shown. Find the equation of the circle with largest area that can be drawn inside the square. Image in the link: http://prntscr.com/elnty

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Question 1073399: A square OABC is drawn with vertices as shown. Find the equation of the circle with largest area that can be drawn inside the square.
Image in the link: http://prntscr.com/elntyz
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
HINT: Midpoint of the entire square
Another HINT: Midpoint of any of the sides


Middle of OB same as CA
(0,2)
and this is the center of the circle.

Middle of segment BA
x=%280%2B2%29%2F2=1
-
y=%284%2B2%29%2F2=3
-
The point (1,3) is on the circle.


Distance From Center to (1,3) gives the radius.
r, radius
r%5E2=%281-0%29%5E2%2B%283-2%29%5E2
r%5E2=1%2B1
r%5E2=2


EQUATION
%28x-0%29%5E2%2B%28y-2%29%5E2=1
highlight%28x%5E2%2B%28y-2%29%5E2=1%29

Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
.
The center of the circle is at the point (x,y) = (0,2).

The radius of the circle is   sqrt%282%29.

The equation of this circle is

x%5E2+%2B+%28y-2%29%5E2 = 2.


Ignore the answer by  "josgarithmetic",  since it is nonsensical.