Question

The centres of two circles of radii 3 cm and 2 cm are 8 cm apart. Find the length of the common tangent.

• A. 39 cm
• B. $\sqrt{39}cm$
• C. 64 cm
• D. 25 cm

Answer 1

The correct option is B

$\sqrt{39}cm$

In the figure, MN is the common tangent. A and B are the centres of the two circles with radii 3 cm and 2 cm respectively.

AB=8 cm. AM=3 cm and BN=2 cm. Draw BC perpendicular to AM extended forward.

Since BCMN is a rectangle, CM=BN=2 cm.

Now, AC=AM+CM=3 cm+2 cm=5 cm.

In ABC, $A{B}^2=B{C}^2+A{C}^2$

$B{C}^2=A{B}^2-A{C}^2$

$=8^2-5^2$

$BC=\sqrt{39}cm$