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Math Help - Circle Geometry Help - Very Difficult

  1. #1
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    Circle Geometry Help - Very Difficult

    Hi there,

    Need some help with this circle geometry question:

    Point P is marked inside a regular hexagon ABCDEF so that Angle BAP = Angle DCP = 50 degrees.

    Find the size of angle ABP.

    Thanks!
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  2. #2
    Senior Member MaxJasper's Avatar
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    Lightbulb Re: Circle Geometry Help - Very Difficult

    ABP=80 deg
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    Last edited by MaxJasper; September 9th 2012 at 12:20 AM.
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  3. #3
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    Re: Circle Geometry Help - Very Difficult

    Quote Originally Posted by MaxJasper View Post
    ABP=80 deg
    Care to elaborate? What theorems? How did you arrive at that conclusion?
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  4. #4
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    Re: Circle Geometry Help - Very Difficult

    We know that the interior angles of a regular hexagon are 120 degrees.
    The triangles with apex P are congruent by side-angle-side.
    So all the base angles are 50d or 70d.
    So angle ABP is 70 degrees
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  5. #5
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    Re: Circle Geometry Help - Very Difficult

    How do you know that the triangles are congruent? They are most certainly not. Only one side is equal in each of the triangles, that is all you know.
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