To find: The diameter of a
The diameter of the circle is
Given data: Three points
Method/Formula used:
The perpendicular bisectors of two chords of a circle meet at the center of the circle. The equation of line with slope m and passing through point
Calculations:
Three points
Lines OA and AB are two chords of the circle and M and N are the mid points of chords OA and AB respectively. Their bisectors MC and NC meet at point C , which is the center of the circle passing through points
The midpoint of chord OA is
Therefore, equation of line MC , with slope 3 and passing through point
The midpoint of chord AB is
Therefore, slope of line NC,
Therefore, equation of line NC , with slope -1 and passing through point
Now, solve equation (1) and (2), equating y as,
Substitute, -2 for x in equation (2),
Therefore, the center of the circle is
Therefore, the diameter of the circle is
Chapter 8 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
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