Question : Two circles with radii of 25 cm and 9 cm touch each other externally. The length of the direct common tangent is:
Option 1: 34 cm
Option 2: 30 cm
Option 3: 36 cm
Option 4: 32 cm
Correct Answer: 30 cm
Solution :
Length of common tangent = $\sqrt{d^2-(r_1-r_2)^2}$,
where $d$ is the distance between the two circles, $r_1$ is the larger radius, and $r_2$ is the smaller radius of the two circles.
Here, $d=25+9=34\ \text{cm}$
$r_1=25\ \text{cm}$ and $r_2=9\ \text{cm}$
Putting values in the equation, we get,
Length of common tangent $=\sqrt{34^2-(25-9)^2}=\sqrt{1156-256}=\sqrt{900}=30\ \text{cm}$
Hence, the correct answer is 30 cm.
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