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 = 90^{0}