We are given
AC=BC(i), and
AB^2=2AC^2 (ii)
We can rewrite equation (ii) as
AB^2=AC^2 + AC^2
AB^2=AC^2 +BC^2 (iii) (Given AC=BC so also AC^2=BC^2)
We know that the equation matches with the Pythagoras equation
So triangle ABC is a isosceles right trianglewith AB as hypotenus and right angled at C that is
angle ACB = 900