SOLUTION: find the center and radius of the circle passes through (2,3), (6,1) and (4,3).
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Question 771666: find the center and radius of the circle passes through (2,3), (6,1) and (4,3).
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The center of the circle is at the same distance from the 3 points.
That means it's on the perpendicular bisector of the segments connecting those 3 points.
Points (2,3) and (4,3) are on a horizontal segment with midpoint at (3,3).
The perpendicular bisector of that segment is the vertical line that passes through (3,3), with equation .
All we need now is a second segment and its perpendicular bisector.
The midpoint of the segment connecting (6,1) and (4,3) is
(,) or (5,2).
The slope of the line connecting (6,1) and (4,3) is
The slopes of perpendicular line multiply to yield , so the slope of the perpendicular bisector to the segment connecting (6,1) and (4,3) is
The perpendicular bisector to the segment connecting (6,1) and (4,3) has the equation
(in point-slope dorm based on midpoint (5,2).
-->-->
The intersection of the two perpendicular bisectors found is the solution to
, and that is , the point (3,0),
The center of the circle is .
The radius is the distance from that point to any of the 3 given points.
For example, using (4,3),
-->-->-->.
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