Two circles of radii 16cm and 9 cm touch each other externally. Find the length of the direct common tangent.

Question

This is question from Theoritical Geometry. 

Answer 1

1)  Please check the spelling of the adjective 'theoritical'--I suspect that's an error.  If not, then I will have learned something.

 

2)  If you draw this figure, you'll see that there is a quadrilateral whose vertices are the two points of tangency of the common external tangent and the two centers of the two touching circles.

 

If you divide that quadrilateral into one rectangle (two sides of length of common tangent, other sides are equal to 9) and then a right triangle one of whose legs is 7 (length 16 - 9), and hypotenuse 25 = 16+9, then the second leg of said rt triangle must be 24*, and this is congruent to the length of the common tangent.  

 

*  Using the well known Pythagorean triple 7-24-25