Question

Find the coordinates of the point which is equidistant from the three vertices $A$($2x,0)O(0,0)\mathrm{and}B(0,2y)of∆$ AOB .

Answer 1

It is known that, in a right angled triangle midpoint of the hypotenuse is equidistant from ots vertices.

Suppose D be the midpoint of the hypotenuse AB.
The coordinates of D are$\left(\frac{2x+0}{2},\frac{0+2y}{2}\right)=\left(x,y\right)$.