A right angled isosceles triangle is inscribed in the circle x²+y²-4 x-2y-4=0 then length of the side of the triangle is

Equation of the given circle is $x^2+y^2$−4x−2y−4=0

The radius of the circle is $\sqrt{4+1+4}=3$

The length of hypotenuse of right angled isosceles triangle inscribed in the circle is equal to diameter, it is equal to 2r=6

Let a be the length of the side of right angled Isosceles triangle

Hence

 $$\begin{gathered} a^2+a^2=4r^2 \\ \Rightarrow 2a^2=36 \\ \Rightarrow a^2=18 \\ \Rightarrow a=3\sqrt{2} \end{gathered}$$

   Therefore, the length of the side is $3\sqrt{2}$