Coordinate Geometry

 

 

B is at the oriigin , so B(0,0) ,

BC lies on the x axis and BC = a , so C(a, 0)

Let A (x,y)

So AB ² = x ²+ y² = a ²  so y² = a ^{2  -} x²

AC² = (x -a ) ² + y ²   =  a ²

Substituting, y² = a ^{2  -} x²

 (x -a ) ² + a ^{2  -} x²   =  a ²

So a² - 2ax = 0

a²  =  2ax

x = a/ 2, A(a/2  ,  a /2)