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Math Help - question on properties of circle 6

  1. #1
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    question on properties of circle 6

    Referring to the attached pic:
    A quadrilateral ACQR is inscribed in a circle. Diagonals are drawn to intersect at T such that angle ATR = 76^o
    Both S, P and B are points outside the circle.
    AC and RQ are extended to meet at P such that angle APR = 30^o
    CQ and AR are extended to meet at B such that angle ABC = 46^o
    QC is extended to S, forming triangle SAC where SC = AC

    Find the angle ASC.
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  2. #2
    MHF Contributor red_dog's Avatar
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    \widehat{ART}=\frac{m(arcAR)+m(arcCQ)}{2}=76

    \widehat{APR}=\frac{m(arcAR)-m(arcCQ)}{2}=30

    Then m(arcAR)=106, \ m(arcCQ)=46

    \widehat{ATC}=\frac{m(arcAC)+m(arcQR)}{2}=104

    \widehat{ABC}=\frac{m(arcAC)-m(arcQR)}{2}=46

    Then m(arcAC)=150, \ m(arcQR)=54

    Now, \widehat{ACQ}=\frac{m(arcQR)+m(arcAR)}{2}

    Can you continue?
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