Question : If the distance between the centres of two circles is 12 cm and the radii are 5 cm and 4 cm, then the length (in cm) of the transverse common tangent is:
Option 1: $9$
Option 2: $\sqrt{143}$
Option 3: $\sqrt{63}$
Option 4: $7$
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Correct Answer: $\sqrt{63}$
Solution :
Given, the distance between the centres of two circles is 12 cm ($d$) and the radii are 5 cm ($r_1$) and 4 cm ($r_2$).
Length of the transverse common tangent line to the circle
= $\sqrt{d^2-(r_1+r_2)^2}$
= $\sqrt{12^2-(5+4)^2}$
= $\sqrt{144-81}$
= $\sqrt{63}\ \text{cm}$
Hence, the correct answer is $\sqrt{63}$.
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