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Math Help - Angles in circle

  1. #1
    Member helloying's Avatar
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    Angles in circle

    thank you
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  2. #2
    MHF Contributor
    Grandad's Avatar
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    Angles in circles

    Hi -

    This is a bit tricky. You need to suppose angle FCD = x. Then angle BCE is also x (vertically opposite angles).

    Then you can use the following facts to find an equation for x:

    • The exterior angle of a triangle is equal to the sum of the interior opposite angles. (So, for instance, angle ADC = 32 + x)
    • The opposite angles of a cyclic quadrilateral are supplementary. (So, for instance, angle ADC + angle ABC = 180 degrees.)

    When you've got x you can now use the fact that:

    • The exterior angle of a cyclic quadrilateral is equal to the opposite interior angle. (So, for instance, angle DAB = angle FCD.)

    I hope you can work it out from here.

    Grandad
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