Please help me with these questions:

1. If one side of a cyclic quadrilateral is produced, prove that the exterior angle, so formed is equal to the opposite interior angle of the quadrilateral.

2. ABC is an isosceles triangle. D and E are any points of AB and AC respectively. If DE||BC (DE is parallel to BC), prove that DBCE is a cyclic quadrilateral.

3. If AC and BD are two equal chords on the opposite sides of diameter AB of a circle with centre O, prove that AC||BD.

4. Two equal circles intersect at A and B. Through A straight line MAN is drawn terminated by the circumferences show that BM=BN.

Thanks in advance for your help!