# In the given figure, two identical circles of radius 4 cm touch each o

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

A. 3√3

B. 2√6

C. 4√2

D. 6√2

### Right Answer is: C

#### SOLUTION

Since radius of both circle is equal

So distance AB = 4 + 4 = 8, PQ = 16

∴ AP = AB + BP = 8 + 4 = 12

In ∆ ASP, ∠ ASP = 90^{o}

AP^{2} = AS^{2} + PS^{2}

PS^{2} = 12^{2} – 4^{2}= 128

PS = 8

In ∆ PQR &∆ ASP

∠ P = ∠ P

∠ ASP = ∠ RQP

∠ SAP = ∠ PRQ

∆ PRQ ~ ∆ PAS

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In the given figure, two identical circles of radius 4 cm touch each o