find the circumcentre of the Triangle formed by points (1,3) , (0,-2) , (-3,1)
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circumcentre of triangle is equidistant from vertices , so
A(1,3),B(0,-2),C(-3,1) are equidistant from O .
let the coordinates of O be (x,y) .
AO=BO
(x-1)²+ (y-3)²=(x-0)²+(y+2)²
x²+1-2x+y²+9-2y=x²+y²+4-4y
10-2x-2y=4-4y
2x-2y=6
x-y=3. equation - (i)
CO=A O
(x-1)²+(y-3)²=(x+3)²+(y-1)²
x²+1-2x+y²+9-6y=x²+9+6x+y²+1-2y
-6y-2x=6x-2y
8x+4y=0
2x+y=0. equation -(ii)
by elimination method
3x=3
x=1
put value of x in equation (i)
1-y=3
y=-2
coordinates of circumcentre =(1,-2)
A(1,3),B(0,-2),C(-3,1) are equidistant from O .
let the coordinates of O be (x,y) .
AO=BO
(x-1)²+ (y-3)²=(x-0)²+(y+2)²
x²+1-2x+y²+9-2y=x²+y²+4-4y
10-2x-2y=4-4y
2x-2y=6
x-y=3. equation - (i)
CO=A O
(x-1)²+(y-3)²=(x+3)²+(y-1)²
x²+1-2x+y²+9-6y=x²+9+6x+y²+1-2y
-6y-2x=6x-2y
8x+4y=0
2x+y=0. equation -(ii)
by elimination method
3x=3
x=1
put value of x in equation (i)
1-y=3
y=-2
coordinates of circumcentre =(1,-2)
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