In the given figure, two identical circles of radius 5 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) or RQ?

\(5\sqrt {2}\)

SP² = 10 × 20

SP² = 200

SP = \(10\sqrt {2}\)cm

RP = (\(10\sqrt {2}+a\))

RQ = RS = a (tangent from same point)

(RQ)² + (20)² = (RP)²

a² + 400 = (\(10\sqrt {2}+a\))²

a² + 400 = 200 + a² + \(20\sqrt {2}a\)

200 = \(20\sqrt {2}a\)

\(a=\frac{10}{\sqrt {2}}=\frac{10\sqrt {2}}{2}=5\sqrt {2}cm\)