# Double Trouble

Geometry Level 5

The alternate (interior) angles of a regular pentagon are joined to form another regular pentagon. The ratio of the area of the smaller pentagon to the area of the bigger pentagon in simplest form is $$( a - \sqrt{b} \times c ) : d,$$ where $$a ,b ,c , d$$ all are pairwise co-prime and $$a>0.$$ Find $$a + b + c + d.$$

×