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Thread: 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 $\displaystyle \angle AOD$ + $\displaystyle \angle BOC$ = 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 $\displaystyle \angle AOD$ + $\displaystyle \angle BOC$ = 180 degrees.

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

    $\displaystyle \angle E = 90^o$ (given)

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

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

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

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

    Grandad
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