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Question : The distance between the centres of two circles having radii 22 cm and 18 cm, is 32 cm. The length (in cm) of the direct common tangent of the two circles is:

Option 1: $2 \sqrt{252} \mathrm{~cm}$

Option 2: $2 \sqrt{152} \mathrm{~cm}$

Option 3: $3 \sqrt{242} \mathrm{~cm}$

Option 4: $3 \sqrt{252} \mathrm{~cm}$


Team Careers360 6th Jan, 2024
Answer (1)
Team Careers360 11th Jan, 2024

Correct Answer: $2 \sqrt{252} \mathrm{~cm}$


Solution : Given: The distance between the centres of two circles having radii 22 cm and 18 cm, is 32 cm.
Let the radius of the bigger circle ($r_1$) = 22 cm
And the radius of the smaller circle ($r_2$) = 18 cm
Distance between the centres of two circles ($d$) = 32 cm
We know,
The length of the direct tangent($l$) = $\sqrt{d^2–(r_1 – r_2)^2}$
⇒ $l=\sqrt{32^2–(22–18)^2}$
⇒ $l=\sqrt{32^2–4^2}$
⇒ $l=\sqrt{1024–16}$
⇒ $l=\sqrt{1008}=2 \sqrt{252} \mathrm{~cm}$
Hence, the correct answer is $2 \sqrt{252} \mathrm{~cm}$.

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