In the given figure, SX is tangent. SX = OX = OR. If QX = 3 cm and PQ = 9 cm. Then what is the value (in cm) of OS ?

Solution (By Examveda Team)

In the given circle,
SX is a tangent
SX² = (XQ) × (PX)
SX² = 3 × [PQ+ QX]
SX² = 3 × [3 + 9]
SX² = 3 × 12
SX² = 36
SX = 6 cm
RO = 6 = OX = SX
∴ OQ = OX - QX and
PO = PQ - OQ
OQ = 6 - 3 = 3 cm and
PO = 9 - 3 = 6 cm
PQ and RS Intersects at O,
∴ PO × OQ = RO × OS
⇒ 6 × 3 = 6 × OS
⇒ OS = 3 cm