Trying to figure out coordinates of isoscleles triangle

Question

I'm programming some application, which heavily depends of geometry. Let's say, in 2D coordinates system I have i.e. :

Bxy = (5,-2)
Cxy = (2,-5)
ABlength = 5.5

Now I need (x,y) of an A (vertex) point. I'm not mathematician, so please, be gentle. Thank you.

Answer 1

HINT:

We have $$(A_x-5)^2+(A_y+2)^2=(A_x-2)^2+(A_y+5)^2=(5.5)^2$$

From $$(A_x-5)^2+(A_y+2)^2=(A_x-2)^2+(A_y+5)^2$$, we can express $A_x$ in terms of $A_y$ linearly.

Put this value in $$(A_x-2)^2+(A_y+5)^2=(5.5)^2$$ to find $A_y$