Since Point B is a point of tangency, there is a right angle being created on the edge of that circle.
This means that the Pythagorean Theorem can be applied to solve for r.
[tex]a^2+b^2=c^2[/tex]
[tex]r^2+24^2=(16+r)^2[/tex]
*A common mistake here is distributing the square to both 16 and r, whereas you should be multiplying 16+r by itself (FOIL).*
[tex]r^2+576=r^2+32r+256[/tex]
The [tex]r^2[/tex]s cancel.
[tex]32r+256=576[/tex]
[tex]32r=320[/tex]
[tex]r=10[/tex]
The radius r of Circle C is 10.
Hope this helps!
