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 ?
Answer & explanation
Correct answer: option 3
∠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