smc

Draw the diagram as shown. Note that the two tangent lines from a single outside point of a circle have the exact same length, so $AB=AC=20$, $BP=PQ$, and $QR=CR$. The perimeter of the triangle is $AP+PR+AR$. Note that $PQ+QR=PR$, so from substitution, the perimeter is $$AP+PQ+QR+AR$$ $$AP+BP+CR+AR$$ $$AB+AC$$ Thus, the perimeter of the triangle is $40$, so the answer is $\boxed{40}$.