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Math Help - question on properties of circle 5

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    question on properties of circle 5

    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.
    Attached Thumbnails Attached Thumbnails question on properties of circle 5-ques-13.jpg  
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