In the given figure, PQRS is a square inscribed in a circle of radius 4 cm. PQ is produced till point Y. From Y a tangent is drawn to the circle at point R. What is the length (in cm) of SY?

Answer: Option A

∠PRQ = 45°
∠ORY = 90°
∠QRY = 45°
RQ = QY
Diagonal = 8 = Diameter
Side $$=\frac{8}{\sqrt{2}}=4\sqrt{2}$$
In ΔSPY,
SY² = SP² + PY²
= 128 + 32
= 160
SY = $$4\sqrt{10}$$