In the picture below, the two circles are externally tangent at point $O$; $BC$ is tangent to both circles; the radius of the large circle is $25$ and the radius of the small circle is $9$. Find $|BC|$.
After some time trying to work out this problem myself, I've looked at the answer provided in the solution manual but still haven't been able to understand the following: the solution seems to take as a given that point $O$ lies on the line connecting the centers of both circles. Although it is intuitive to me, I wonder how to show that the point of tangency between the two circles sits on line $MA$? (This is the first time I've been exposed to the concept of externally tangent circles in the book, so I apologize if the answer to my question is obvious). Thanks.