In the figure given below, a smaller circle touches a larger circle at P and passes through its center O. PR is a chord of length 34 cm, then what is the legth (in cm) of PS?
Explanation:
Let us join QR and SO
OP is the diameter of smaller circle, hence ∠OSP = 90° QP is the diameter of larger circle, hence ∠QRP = 90°
Now, ∆PQR ≈ ∆POS [∠OSP = ∠QRP = 90° and ∠OPS is common angle]
⇒ PR : PS = PQ : PO = 2 : 1
⇒ 34 : PS = 2 : 1
∴ PS = 17 cm.
Hence, option (b).
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