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Math Help - circle

  1. #1
    Senior Member sfspitfire23's Avatar
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    circle

    Given a circle with center 'O' and with two tangents at points 'B' and 'C' which intersect each other at point 'A'. If the angle BAC is given as 55 degrees, then what is the angle BOC?
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  2. #2
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    Quote Originally Posted by sfspitfire23 View Post
    Given a circle with center 'O' and with two tangents at points 'B' and 'C' which intersect each other at point 'A'. If the angle BAC is given as 55 degrees, then what is the angle BOC?
    If the tangents touch at B and C,
    then what measurements are the angles OBA and OCA ?

    The shape ABOC contains 2 triangles.
    Hence, what is the sum of the angles OAC, OCA, OAB, OBA, AOB and AOC ?

    This sum must equal the sum of the angles BAC, ABO, ACO and BOC.

    Hence, angle BOC can be found.
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