SOLUTION: Find an equation for the circle: the points (6,5), (7,2), (9,6), and (10,3) are verices of an inscribed square

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Question 214192: Find an equation for the circle: the points (6,5), (7,2), (9,6), and (10,3) are verices of an inscribed square
Answer by solver91311(24713) (Show Source):
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If a square is inscribed in a circle, a diagonal of the square is a diameter of the circle. The midpoint of a diameter is the center of a circle.

The segment with endpoints (6,5) and (10,3) is a diagonal of the square. Use the midpoint formula:

and

and

So the midpoint of the diagonal, hence the midpoint of a diameter, hence the center of the circle is at (8, 4)

The measure of a radius of the circle is the distance from the center to any of the four vertices. Use the distance formula:

The equation of a circle with center at and radius is:

So:

John