Determine third point of Right Triangle when two points and all sides are known and $A\hat BC=90$

Question

I have two points and all sides of right triangle

I need find A point

\begin{gather*} |AB| = 1 \\ |BC| = 1 \\ |AC| = \sqrt{1^2 + 1^2} = \sqrt2 \\ A(?,?) \\ B(0,0) \\ C(1,0) \\ \\ |AB| = 1 \\ |BC| = \sqrt{1^2 + 1^2} = \sqrt2 \\ |AC| = \sqrt{1^2 + \sqrt2^2} = \sqrt3 \\ A(?,?) \\ B(0,0) \\ C(1,0) \end{gather*}

The angle in $B$ is 90 degrees.

I need a formula to find point $A$. i need infinity loop that create a chain of triangle not just one triangle