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Math Help - Circle Geometry

  1. #1
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    Exclamation Circle Geometry

    Hey guys

    Two perpendicular chords AB and CD of a circle, centre O, intersect at E. Prove that \angle AOD + \angle BOC = 180 degrees.

    Could someone please help me? I can't seem to work this one out.
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  2. #2
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    Hello xwrathbringerx
    Quote Originally Posted by xwrathbringerx View Post
    Hey guys

    Two perpendicular chords AB and CD of a circle, centre O, intersect at E. Prove that \angle AOD + \angle BOC = 180 degrees.

    Could someone please help me? I can't seem to work this one out.
    In \triangle ACE:

    \angle E = 90^o (given)

    \Rightarrow  \angle ACD+\angle BAC = 90^o (angle sum of triangle)

    But \angle AOD = 2\angle ACD (angle at centre = twice angle at circumference)

    and \angle BOC = 2\angle BAC (angle at centre = twice angle at circumference)

    \Rightarrow \angle AOD + \angle BOC = 180^o

    Grandad
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