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?
Answer & explanation
Correct answer: option 1
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 = \(20\sqrt {2}a\)
\(a=\frac{10}{\sqrt {2}}=\frac{10\sqrt {2}}{2}=5\sqrt {2}cm\)