Question

Two circles of radii 9 cm and 4 cm touch each other externally. Find the length of their direct common tangent.

• A. 13 cm
• B. 12 cm
• C. 10 cm
• D. 11 cm

Answer 1

Answer:

B. 12 cm

To find the length of the direct common tangent of two circles touching externally, we can use the formula:

$L = \sqrt{d^2 - (R - r)^2}$

Where:

• $R$ = radius of the first circle ($9\text{ cm}$)

• $r$ = radius of the second circle ($4\text{ cm}$)

• $d$ = distance between the centers of the two circles ($R + r$, since they touch externally)

Step-by-Step Calculation

1. Find the distance between the centers ($d$):

   
   

   $d = 9 + 4 = 13\text{ cm}$

2. Find the difference between the radii ($R - r$):

   $R - r = 9 - 4 = 5\text{ cm}$

3. Substitute into the tangent formula:

   
   $L = \sqrt{13^2 - 5^2}$

   $L = \sqrt{169 - 25}$

   $L = \sqrt{144} = 12\text{ cm}$

Answer

The length of the direct common tangent is $12\text{ cm}$.