Question : The distance between the centres of two circles of radii 2 cm and 6 cm is 5 cm. Find the length of the direct common tangent.
Option 1: $6 \mathrm{~cm}$
Option 2: $3 \mathrm{~cm}$
Option 3: $9 \mathrm{~cm}$
Option 4: $\frac{5}{2} \mathrm{~cm}$
Correct Answer: $3 \mathrm{~cm}$
Solution :
Given: The distance between the centres of two circles of radii 2 cm and 6 cm is 5 cm
The length of the direct common tangent between two circles $ = \sqrt{d^2 - (r_1 - r_2)^2}$ where $d$ is the distance between the centres of the two circles and $r_1$ and $r_2$ are the radii of the two circles.
The length of the direct common tangent between two circles $= \sqrt{(5)^2 - (2 - 6)^2} = \sqrt{25 - 16} = \sqrt{9} = 3 \mathrm{~cm}$
Hence, the correct answer is $3 \mathrm{~cm}$.
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