Question 36
In this figure the radius of the circle is equal to the altitude of the equilateral triangle $ABC.$ The circle is made to roll along the side $AB,$ remaining tangent to it at a variable point $T$ and intersecting lines $AC$ and $BC$ in variable points $M$ and $N,$ respectively. Let $n$ be the number of degrees in arc $MTN.$ Then $n,$ for all permissible positions of the circle:
