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Question

Find the circumcentre of the triangle with the vertices A (-3,4) , B (3,4) and C (-4,-3). What is the circumradius of the circle?

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Solution

We want the equation of circle to pass through points A(3,4),B(3,4) and (4,3)
The equation of a circle is x2+y2+ax+by+c=0
From the coordinates of the three given points we get three equations.
(3)2+423a+4b+c=0
32+423a+4b+c=0
(4)2+324a+3b+c=0
we can simplify the above equation -
341341431abc=252525
solving the above matrix equation using craner's rule a=0, b=0 and c=25
Putting there values a,b and c in general form we write required equation of circle x2+y225=0
On center radius form (x+0)2+(y+0)2=25
Center of circle is (0,0) and radius =5.
Hence, the answer is 5.



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