Question

The distance between the centres of two circles having a radii $4.5$ cm and $3.5$ cm respectively is $10$ cm. What is the length of the transverse common tangent of these circles?

• A. $8$ cm
• B. $7$ cm
• C. $6$ cm
• D. None of the above

Answer 1

The correct option is D None of the above

Length of the transverse common tangent is $LM$.
Now $LM=CB$

$BM=3.5$ cm ....Given

Thus length of AC $=AL-BM=4.5-3.5=1$ cm

Thus $LM=CB=$ $\sqrt{A{B}^2-A{C}^2}$
$=\sqrt{{10}^2-1^2}=\sqrt{99}$
$=3\sqrt{11}$ cm

Therefore, the length of transverse common tangent of these circles is $3\sqrt{11}$.cm.