document.write( "Question 1207325: Find the equation of the circle which is circumscribed about the triangle, whose vertices are B (3,0), O (15,4) AND X (17,-2)
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Algebra.Com's Answer #845141 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The responses from the other tutors show a standard solution, finding the center of the circle by finding the intersection of the perpendicular bisectors of two sides of the triangle.

\n" ); document.write( "For this particular triangle, there is a much easier path to the answer.

\n" ); document.write( "Draw a sketch of the triangle roughly to scale and observe that BO and OX appear to be perpendicular. Verify that they are by finding that the slopes of those two segments are 1/3 and -3.

\n" ); document.write( "That makes angle O a right angle; and that makes BX the diameter of the circumscribed circle.

\n" ); document.write( "The center of the circle is then the midpoint of BX, which is (10,-1).

\n" ); document.write( "Use the Pythagorean Theorem (aka distance formula) to find that the radius is sqrt(50).

\n" ); document.write( "Then the equation of the circumscribed circle is

\n" ); document.write( "ANSWER: $\"%28x-10%29%5E2%2B%28y%2B1%29%5E2=50\"$

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