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anonymous
 4 years ago
If the vertices of triangle ABC are A(2, 1), B(0, 2) and C(4, 3), what are the coordinates of the circumcenter?
anonymous
 4 years ago
If the vertices of triangle ABC are A(2, 1), B(0, 2) and C(4, 3), what are the coordinates of the circumcenter?

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mathmate
 4 years ago
Best ResponseYou've already chosen the best response.0It is a very obtuse triangle. The three points lie almost on a straight line. Back to basics, a circumcentre is a point which is equidistant to all three points, so that it is the centre of a circle that passes through all three points. Using Pythagoras theorem, and assuming the required circumcentre is at (x0,y0), then R=radius of circumcircle and R^2=(XaX0)^2+(YaY0)^2=(XbX0)^2+(Yby0)^2=(Xcx0)^2+(Ycy0)^2 You will have a system of two linear equations (since all the x0^2 and y0^2 terms cancel out) from which you can solve for X0 and Y0. (XaX0)^2+(YaY0)^2=(XbX0)^2+(Yby0)^2 reduces to 6y4x+1=0 and (XbX0)^2+(Yby0)^2=(Xcx0)^2+(Ycy0)^2 reduces to 10y+8x21=0 from which you can solve for X0 and Y0. Hint: X0+Y0=24 (for checking purpodw:1327108062011:dwses).
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