Find the co-ordinates of the circumcenter of the triangle whose vertices are A(−2,3), B(6,−1), C(4,3).

5.4 · Q70

Q. Find the co-ordinates of the circumcenter of the triangle whose vertices are A(-2,3), B(6,-1), C(4,3).

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Let $O(x,y)$ be equidistant from $A(-2,3)$ , $B(6,-1)$ , $C(4,3)$ . From $OA^2=OB^2$ : $(x+2)^2+(y-3)^2=(x-6)^2+(y+1)^2$ , expanding and simplifying gives $16x-8y-24=0$ , i.e. $2x-y-3=0$ ...(i). From $OB^2=OC^2$ : $(x-6)^2+(y+1)^2=(x-4)^2+(y-3)^2$ , expanding and simplifying gives $-4x+8y+12=0$ , i.e. $x=2y+3$ ...(ii). Substituting (ii) …

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Q.Find the co-ordinates of the circumcenter of the triangle whose vertices are A(−2,3), B(6,−1), C(4,3).

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Q.Find the co-ordinates of the circumcenter of the triangle whose vertices are A(−2,3), B(6,−1), C(4,3).

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