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Question

The verties of a triangle are O (0,0), A(a,0)andB(0,b). Write the coordinates of its circumcentre.

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Solution

Let P(x,y) be the circumcentre of the given trianlge,ThenPO2=PA2=PB2(x0)2+(y0)2=(xa)2+(y0)2x2+y2=x2+a22ax+y22ax=a2x=a2and,PO2=PB2(x0)2+(y0)2=(x0)2+(yb)2x2+y2=x2+y2+b22by2by=b2y=b2Hence,coordinates of circumcentre are (a2,b2)


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