Question

How to find the circumcenter of a right triangle from sides equations?

Answer 1

heya mate here is your answer

Midpoint of a line in the triangle = x1+x2/2, y1+y2/2
Midpoint of AB = 5+6/2, 7+6/2 = (11/2, 13/2)
Midpoint of BC = 6+2/2, 6-2/2 = (4, 2
Midpoint of CA = 2+5/2, -2+7/2 = (7/2, 5/2) Midpoint of a line in the triangle = x1+x2/2, y1+y2/2

formula y2-y1/x2-x1 for slope

Slope of AB (m) = 6-7/6-5 = -1.
Slope of BC (m) = -2-6/2-6 = 2.
Slope of CA (m) = 7+2/5-2 = 3.

Formula to find the circumcenter equation y-y1 = m(x-x1)

y-13/2 = 1(x-11/2)

, we get the equation -x + y = 1 -------------1

Similarly, we have to find the equation of the perpendicular bisectors of the lines BE and CF.

For BC with midpoints (4,2) and slope -1/2
y-2 = -1/2(x-4)

By solving the above, we get the equation x + 2y = 8 -------------2
For CA with midpoints (7/2,5/2) and slope -1/3
y-5/2 = -1/3(x-7/2)

By solving the above, we get the equation x + 3y = 11 ------------3


Find the value of x and y by solving any 2 of the above 3 equations.
In this example, the values of x any y are (2,3) which are the coordinates of the Circumcenter (o).



This is an example so that u can understand how to do remainimg sums !!


i hope ot helps uh