# How to find the center of a circle given the three points (-3,5); (3,3); (11,19)?

##### 2 Answers

The perpendicular bisectors of two secant lines intersect at the center.

#### Explanation:

Find the slopes of the lines through two pairs of points.

Find the midpoints of those lines

The perpendicular bisectors are the lines through the midpoints with slopes equal to the negative reciprocals of the slopes of the secant lines.

Find the equations of the perpendicular bisectors.

Now find the intersection of the lines whose equations you just found.

The secant joining

The equation of the perpendicular bisector of the secant is

It is left to the reader to verify that the secnt jining

The lines

intersect at

The center (a, b) is at the same distance = radius, from each of the three points on the circle. This gives a = 3 and b = 13..

#### Explanation:

The points are equidistant from the center (a, b). Equating squares of the distances,

From the first two,

solving, (a, b) = (3, 13)...