1) In a cyclic quadrilateral, the sum of opposite angles is .
Let be a cyclic quadrilateral, such that .
We have and . Then
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!