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: $\sqrt{132}$
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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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