Question : Two circles of radius 2.4 cm and 4 cm, respectively, have a common tangent. The distance between the centres of the two circles is 6.5 cm. If the common tangent does not intersect the line joining the centres, then find the length of a common tangent to the circles.
Option 1: 6.0 cm
Option 2: 6.2 cm
Option 3: 6.1 cm
Option 4: 6.3 cm
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Correct Answer: 6.3 cm
Solution :
Given: $r{_1}=2.4$ cm, $r{_2}=4$ cm, $d=6.5$ cm
Length of the common tangent
= $\sqrt{d^2-(r{_1}-r{_2})^2}$
= $\sqrt{6.5^2-(2.4-4)^2}$
= $\sqrt{42.25-(1.6)^2}$
= $\sqrt{42.25-2.56}$
= $\sqrt{39.96}$
= $6.3$ cm
Hence, the correct answer is 6.3 cm.
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