Question : The distance between the centres of two circles having radii 16 cm and 8 cm, is 26 cm. The length (in cm) of the direct common tangent of the two circles is:
Option 1: $2 \sqrt{132}$
Option 2: $\sqrt{153}$
Option 3: $2 \sqrt{153}$
Option 4: $\sqrt{132}$
Correct Answer: $2 \sqrt{153}$
Solution :
Given:
The radius of the bigger circle $r_1= 16$
The radius of the smaller circle $r_2= 8$
Distance between the centres, $d = 26$
So, the length of the direct common tangent, $l = \sqrt{d^2-(r_1-r_2)^2}$
$= \sqrt{26^2-(16-8)^2}$
$=\sqrt{676-64}$
$= \sqrt{612}$
$=2\sqrt{153}$
So, the length of the common tangent is $2\sqrt{153}$.
Hence, the correct answer is $2\sqrt{153}$.
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