In the given figure PQRS is a square inscribed in a circle of radius 6 cm, PQ is parallel till point Y. From Y a tangent is drawn to the circle at point R. What is the length (in cm) of SY ?

\(\sqrt[6]{10}\)

∠PRQ = 45°    (∴ square)

∠PRY = 90°    (∴ RY is tangent)

∠QRY = 45°

RQ = QY

Diagonals of square = \(\sqrt {2}\)a

⇒ \(\sqrt {2}\) a = 12 ⇒ a = 6\(\sqrt {2}\)

in ΔSPY

SY² = PY² + SP²

      = (12\(\sqrt {2}\))² + (16\(\sqrt {2}\))²

SY² = 288 + 72 = 360

SY = 36 × 10 

⇒ SY = 6\(\sqrt {10}\) cm