Discussion

Question:

In the given figure, two identical circles of radius 4 cm touch each other. A and B are the centers of the two circles. If RQ and RS are tangents to the circle, then what is the length (in cm) of RQ?

Explanation:

PQ = 4 + 4 + 4 + 4 = 16 cm

PA = 4 + 4 + 4 = 12 cm

In ∆ASR, PA² = AS² + PS²

⇒ 144 = 16 + PS²

⇒ PS = 8√2

Now, ∆PQR ~ ∆PSA

⇒ $\frac{R Q}{A S} = \frac{Q P}{P S}$

⇒ $\frac{R Q}{4} = \frac{16}{8 \sqrt{2}}$

⇒ RQ = 4√2 cm

Hence, option (c).

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