document.write( "Question 925600: A circle is circumscribing a triangle formed by the lines y=0, y=x and 2x+3y=10. Find the equation of the circle \n" ); document.write( "

Algebra.Com's Answer #561691 by KMST(5328) $\"\"$ $\"About$

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The lines intersect at O(0,0), A(2,0), and B(0,10/3).
\n" ); document.write( "Those are the vertices of triangle ABO.
\n" ); document.write( "The center of the circle circumscribing ABO is the intersection point of the perpendicular bisectices of the sides.
\n" ); document.write( "The bisectrix of horizontal side OA is the vertical line x=5/2, which passes through (0,5/2), the midpoint of OA.
\n" ); document.write( "The bisectrix of vertical side OB is horizontal line y=5/3, which goes through (0,5/3),the midpoint of OB.
\n" ); document.write( "Those bisectrices intersect at (5/2,5/3) , and that is the center of the circle.
\n" ); document.write( "The radius $\"R\"$ is the distance from the center to each vertex.
\n" ); document.write( "Using vertex O, that distance squared is
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\n" ); document.write( "So, the equation if the circle is
\n" ); document.write( " $\"%28x-5%2F2%29%5E2%2B%28y-5%2F3%29%5E2=325%2F36\"$ \n" ); document.write( "

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