Latest self Aptitude Question SOLUTION: Two circles of radius 4cm, and 9cm touch each other externally. A common tangent AB is drawn to these two circles, A and B lie on the two circles respectively. Then the radius of t

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(#M40013789) SELF question Self Keep an EYE

Two circles of radius 4cm, and 9cm touch each other externally. A common tangent AB is drawn to these two circles, A and B lie on the two circles respectively. Then the radius of the circle which touches the given circles, and also whose tangent is line AB is(a) 1.32 cm (b) 1.44 cm (c) 1.56 cm (d) 1.68 cm

Arjun (11 years ago)

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Vinay Sipani   (11 years ago)

b) 1.44 cm

One way of solving is
9 and 4 are perfect square=>radius of other circle also a perfect square=1.44cm

The other way is
L = √(4×9×4) = 12 cm
The new circle is b/w the tangent and two circles and radius = r

The length of tangent b/w r and 9cm circles = √(4×r×9) = L1
The Length of tangent b/w r and 4cm circles = √(4×r×4) = L2
Also (L1 + L2) = 12
=> √(4×r×9)+ √(4×r×4) = 12
=> 10√r = 12
=> r = 1.44 cm

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