I have problems in solving the following problem:
Consider two circles which have only one point $A$ in common, i.e. which are tangent to each other. Now consider two lines through A, such that the lines meet the circles at further points $B,C,D,E$. I want to prove that the lines $DE$ and $BC$ are parallel lines ($D,E$ being points on one circle and $B,C$ on the other).
I tried to use theorems like the inscribed angle theorem, but I was not succesfull so far. Does someone know how to solve this problem?
If it is possible, I only want to use geometric arguments, and not analytical arguments. Does this result have any name?