In a circle, PQ and RS are two diameters that are perpendicular to each other. Find the length of the chord PR.

Let the radius of the circle = r

PQ and RS are two diameters that are perpendicular to each other

$$=$$>  PQ = RS = 2r

$$=$$>  r = $$\frac{\text{PQ}}{2}$$

In $$\triangle\ $$OPR,

$$\text{PR}^2=\text{OR}^2+\text{OP}^2$$

$$=$$>   $$\text{PR}^2=r^2+r^2$$

$$=$$>   $$\text{PR}^2=2r^2$$

$$=$$>   $$\text{PR}=\sqrt{2}r$$

$$=$$>   $$\text{PR}=\sqrt{2}\times\frac{PQ}{2}$$

$$=$$>   $$\text{PR}=\frac{PQ}{\sqrt{2}}$$

Hence, the correct answer is Option D