Math Arguments

Two Tangents

Given: 2 common tangent lines, one external and one internal.

The question was raised as to whether the large circle could be tangent to both lines at the intersection point. What do you think?

The fun part, of course, is "Can you explain that to the English teacher?" (force them to be clear but not too technical). If those are tangents, can the circle go through the intersection point, even if not tangentially?