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Math Help - help needed for question on circles

  1. #1
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    help needed for question on circles

    hi all, here goes the question. A,b,c,d are four points on the circumference of the circle. P is the point of intersection of lines ac and bd. St is the tangent of the circle at point d. Given that angle adt=60 degrees and angle cdb=40 degrees, find angle apd. The centre of circle is not given.
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  2. #2
    MHF Contributor Unknown008's Avatar
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    Hm... Scizor... you had a metal coat?

    Okay, serious things now.

    Make a sketch.

    You'll see from your sketch that angle ADB is equal to (90 - 60). 90 because ST is a tangent and this is divided into two angles, one being 60 degrees.

    Then, using the properties of angles in a circle, we know that angle CBD and angle CAD are equal, hence, angle CAD = 40 degrees (Which is also angle PAD)

    Now, you'll also see that PAD forms a triangle. You have angle PAD, angle PDA and you need to find angle APD. Can you find it?

    The answer is:

    Spoiler:
    Angle APD = 180 - (40+60) = 80 degrees
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  3. #3
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    just a question, why are you so sure that p is indeed the centre of the circle? Otherwise all the properties of circle cannot be applied then.
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  4. #4
    MHF Contributor Unknown008's Avatar
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    I'm not assuming that P is the centre of the circle. I'm considering P as a vertex in a triangle.
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  5. #5
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    Quote Originally Posted by Unknown008 View Post
    I'm not assuming that P is the centre of the circle. I'm considering P as a vertex in a triangle.
    oic cheers for your reply. Much appreciated.
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  6. #6
    MHF Contributor Unknown008's Avatar
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    You're welcome
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