Question

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

Answer 1

$\text{Let P(x,y) be the circumcentre of the given trianlge,Then}P{O}^2=P{A}^2=P{B}^2\Rightarrow (x-0{)}^2+(y-0{)}^2=(x-a{)}^2+(y-0{)}^2\Rightarrow x^2+y^2=x^2+a^2-2ax+y^2\Rightarrow 2ax=a^2\Rightarrow x=\frac{a}{2}and,P{O}^2=P{B}^2\Rightarrow (x-0{)}^2+(y-0{)}^2=(x-0{)}^2+(y-b{)}^2\Rightarrow x^2+y^2=x^2+y^2+b^2-2by\Rightarrow 2by=b^2\Rightarrow y=\frac{b}{2}\text{Hence,coordinates of circumcentre are}(\frac{a}{2},\frac{b}{2})$