Question

If the distance between the centres of two circles of radii 3, 4 is 25.  Then the length of the transverse common tangent is
​

Answer 1

Given:

If the distance between the centres of two circles of radii 3, 4 is 25

To find:

The length of the transverse common tangent

Solution:

Here we have to find the length of the transverse common tangent

For this, we have the formula as:

$\sqrt{d^{2}-(r1+r2)^{2}}$

where d is the distance between the centres of the circle which is 25 cm

r1 is the radius of the first circle which is 3 cm

r2 is the radius of the second circle which is 4 cm

now putting the values in the equation we get

$\sqrt{25^{2}-(3+4)^{2}}$

$\sqrt{25^{2}-7^{2}}$

$\sqrt{625-49}$

$\sqrt{576}$

24 cm

The length of the transverse common tangent  is 24 cm