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