AB and CD are two parallel chords of a circle. CA and DB meet, when produced, at X. AD and BC intersect at Y

There are three parts to this question, two of which are already solved and i will post results:

a)YA= YB

b)XA= XB

How must i prove that XY will pass through center?

And just generally, how is this achieved without using co-ordinate geometry, i.e. proving a certain line passes through centre.