Question : The distance between the centres of two circles of radii 6 cm and 3 cm is 15 cm. The length of the transverse common tangent to the circles is:
Option 1: $12\ \text{cm}$
Option 2: $6\sqrt6\ \text{cm}$
Option 3: $7\sqrt6\ \text{cm}$
Option 4: $18\ \text{cm}$
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Correct Answer: $12\ \text{cm}$
Solution :
Given: The distance between the centres of two circles of radii 6 cm and 3 cm is 15 cm.
The length of the transverse common tangent to the circles,
$= \sqrt{d^2-(r_1+r_2)^2}$
$= \sqrt{15^2-(6+3)^2}$
$= \sqrt{225-81}$
$= \sqrt{144}$
$= 12\ \text{cm}$
Hence, the correct answer is $12\ \text{cm}$.
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