Is there a geometric proof to answers about the 3 classical problems? I know that there is a solution to this topic using algebra (for example, this post). 
But I would like to know if there is a geometric proof to show this impossibility.
Thanks.

No such proof is known. Note that this would in fact be meta-geometric: You do not give a construction of an object from givens, but you make a statement about all possible sequences of operations with your drawing instruments. Therefore it is a good idea to classify all points constructable from standard given points. This set of points has no truely geometric properties (after all, they are dense in the standard Euclidean plane, hence arbitrarily good approximations can be constructed) but nice algebraic properties (algebraic numbers with certain properties).
