Question 809979: find the center and radius of the circle circumscribed about the right triangle with vertices (1,1), (1,4) and (7,4).
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! The segment connecting (1,1) and (1,4) is part of the vertical line  .
The segment connecting (1,4) and (7,4) is part of the horizontal line  .
Obviously those are the legs of the right triangle,
the right angle is at point (1,4),
and the segment connecting (1,1) and (7,4) is the hypotenuse.
THE CENTER:
If you are studying circles, maybe you were taught that an angle inscribed in a circle measures half of the central angle that subtends the same arc.
Maybe you were told that the corollary is that the intercepted arc on an inscribed right angle is  and that makes the corresponding chord a diameter.
In that case, you would realize that the the hypotenuse of the triangle is the diameter and its midpoint is the center of the circle.
If you are studying triangles, maybe you were taught that all three perpendicular bisectors of a the sides of a triangle intersect at the circumcenter, the center of the circumscribed circle.
Either way, you find the coordinates of the center as the midpoint of the hypotenuse, or as the intersection of the horizontal and vertical perpendicular bisectors doing the calculations
 and 
THE RADIUS:
The radius is half of the diameter.
The diameter is the segment connecting (1,1) and (7,4),
and you can calculate its length as
So the radius is  = approximately
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