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: $\sqrt{132}$

Question

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: $\sqrt{132}$

Team Careers360 · Accepted Answer

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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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: 2132Option 2: 153Option 3: 2153Option 4: 132

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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: $\sqrt{132}$