Home > Geometry calculators > Coordinate Geometry > Find the circumcentre of a triangle whose vertices are A(4,1),B(-2,-3),C(6,7)

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 Find circumcentre of a triangle whose vertices are A(4,1),B(-2,-3),C(6,7) [ Calculator, Method and examples ]Solution:Your problem -> circumcentre of a triangle whose vertices are A(4,1),B(-2,-3),C(6,7)A(4,1), B(-2,-3) and C(6,7) form a triangle.The center of a circle which passes through the three vertices of a triangle is called circum center.Let P(x,y) be circum center:. PA=PB=PC:. PA^2=PB^2=PC^2Now PA^2=PB^2(x-4)^2+(y-1)^2=(x+2)^2+(y+3)^2(x^2-8x+16)+(y^2-2y+1)=(x^2+4x+4)+(y^2+6y+9)-12x-8y=-43x+2y=1 ->(1)Now PB^2=PC^2(x+2)^2+(y+3)^2=(x-6)^2+(y-7)^2(x^2+4x+4)+(y^2+6y+9)=(x^2-12x+36)+(y^2-14y+49)16x+20y=724x+5y=18 ->(2)The point of intersection of the lines can be obtainted by solving the given equations.3x+2y=1and 4x+5y=183x+2y=1 ->(1)4x+5y=18 ->(2)equation(1) xx 5 =>15x+10y=5equation(2) xx 2 =>8x+10y=36Substracting =>7x=-31=>x=-31/7Putting x=-31/7  in equation (1), we have3(-31/7)+2y=1=>2y=1+(93/7)=>2y=(7+93)/7=>2y=100/7=>y=50/7:. x=-31/7" and "y=50/7:. (-4.43,7.14) is the intersection point of the given two lines.:. P(-4.43,7.14) is circum center.

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