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.