Question

Find the coordinates of the circum centre of the triangle formed by the points O(0,0 ), A(a,0),
B(0, b).​

Answer 1

let circumcentre point C

so AC=BC=CO

AC^2=BC^2=CO^2

by distance formula

AC^2 = BC^2

[(x-a)^2+(y-0)^2] = [(x-0)^2+(y-b)^2]

by solving

x^2+a^2 -2ax+ y^2 = x^2 +y^2+ b^2-2yb

2(by-ax)= b^2 -a^2 ---- (1)

NOW AC^2=OC^2

(x-0)^2 + (y-b)^2 = x^2 + y^2

by solving this equation y=b/2

put the value of y in (1) and we will get x=a/2

So answer is (a/2,b/2)