Another solved problem. Referring to the pic:

A, B, C, D are the points on a circle with the centre O.

AOC is perpendicular to BOD.

E lies on the arc AB; EC intersects with BOD at X.

F lies on the arc BC; FD intersects with EC and AOC at Y and Z, respectively. EXC and FYZD are straight lines.

Given XO = ZO, prove:

(1) EC is perpendicular to FYZD

(2) arc EBF is 0.25 of the circumference of the circle.