Given three points of a circle: (-1,1), (7,-3), (-2,-6).

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Presentation transcript:

Given three points of a circle: (-1,1), (7,-3), (-2,-6). Find the center of the circle.

Given three points of a circle: (-1,1), (7,-3), (-2,-6). Find the center of the circle. Required Geometry: The perpendicular bisector of a chord of a circle will pass through the center of the circle. The midpoint of a line segment connecting the points (a,b) and (c,d) is the point ((a+c)/2, (b+d)/2). That is, find the average of x coordinates and the average of the y coordinates.

Given three points of a circle: (-1,1), (7,-3), (-2,-6). Find the center of the circle. Find two of the three lines determined by pairs of points.

Given three points of a circle: (-1,1), (7,-3), (-2,-6). Find the center of the circle. Find the points on each line halfway between the original points (i.e. midpoints).

Given three points of a circle: (-1,1), (7,-3), (-2,-6). Find the center of the circle. Find the lines perpendicular to each line at the midpoint.

Given three points of a circle: (-1,1), (7,-3), (-2,-6). Find the center of the circle. Find the point of intersection of the perpendiculars (this is the center of the circle).

Radius = 5 Given three points of a circle: (-1,1), (7,-3), (-2,-6). Find the circle. Determine the equation of the circle. Radius = 5