If in the following figure (not to the scale), $$\angle$$ACB = 135$$^\circ$$ and the radius of the circle is $$2\sqrt{2}$$ cm, then the length of the chord AB is:

In cyclic quadrilateral ACBD,

Sum of opposite angles = 180$$^\circ$$

$$=$$>  $$\angle$$ACB + $$\angle$$ADB = 180$$^\circ$$

$$=$$>  135$$^\circ$$ + $$\angle$$ADB = 180$$^\circ$$

$$=$$>  $$\angle$$ADB = 45$$^\circ$$

Angle subtended by an arc at the centre of the circle is twice the angle subtended by the arc at any point on the circle

$$=$$>  $$\angle$$AOB = 2$$\angle$$ADB

$$=$$>  $$\angle$$AOB = 2(45$$^\circ$$)

$$=$$>  $$\angle$$AOB = 90$$^\circ$$

In $$\triangle$$AOB,

OA$$^{2}$$ + OB$$^{2}$$ = AB$$^{2}$$

$$=$$>  $$\left(2\sqrt{2}\right)^2+\left(2\sqrt{2}\right)^2$$ = AB$$^{2}$$

$$=$$>  AB$$^{2}$$ = 8 + 8

$$=$$>  AB$$^{2}$$ = 16

$$=$$>  AB = 4 cm

$$\therefore\ $$Length of the chord = 4 cm

Hence, the correct answer is Option A