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?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 3
SX = OX = OR, QX = 3 cm, PQ = 9 cm
XP = XP + PQ = 3 + 9 = 12
Now,
SX2 = XQ × XP
SX2 = 3 × 12 = 36
SX = 6 = OX = OR
OQ = OX - QX = 6 - 3 = 3 cm
PO = PQ - OQ = 9 - 3 = 6 cm
PQ and RS intersect at O:
So,
PO × OQ = RO × OS
⇒ 6 × 3 = 6 × OS
⇒ OS = 3 cm