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?

A. $$4\sqrt {10} $$

B. $$2\sqrt {10} $$

C. $$6\sqrt {10} $$

D. $$3\sqrt 5 $$

Answer: Option A

Solution (By Examveda Team)

∠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 = $$4\sqrt {10} $$