+23252 There are two externally tangent circles, circle(A) with radius = 10 and circle(B) with radius = 7.
Therefore, AB = 17.
There is an externally tangent line (with both circle(A) and circle(B) on the same side of the line)
XY, where X is the point of intersection with circle(A) and Y is the point of intersection with circle(B).
Therefore, AX = 10 and BY = 7.
Extend both AB and XY so they intersect at point C.
Triangle(ACX) will be similar to triangle(BCY) because they have corresponding congruent angles.
Call BC = x. This makes AC = x + 17.
This means that: AX / BY = AC / BC. ---> 10 / 7 = (x + 17) / x
---> 10x = 7(x + 17) ---> 10x = 7x + 119 ---> 3x = 119 ---> x = 119/3
BC = 119/3
