Question : If the radii of two circles are 7 cm and 4 cm and the length of the transverse common tangent is 13 cm, then the distance between the two centres is:
Option 1: $\sqrt{290}$ cm
Option 2: $\sqrt{190}$ cm
Option 3: $\sqrt{128}$ cm
Option 4: $\sqrt{240}$ cm
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Correct Answer: $\sqrt{290}$ cm
Solution :
Given, $r{_1}$ = 7 cm and $r{_2}$ = 4 cm
The length of the transverse common tangent = 13 cm
The length of a transverse common tangent $=\sqrt{d^2−(r{_1}+r{_2})^2}$
⇒ $13=\sqrt{d^2−(7+4)^2}$
⇒ $13^2=d^2-11^2$
⇒ $169=d^2-121$
⇒ $d^2=290$
⇒ $d=\sqrt{290}$ cm
Hence, the correct answer is $\sqrt{290}$ cm.
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