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Math Help - circle/tangent/chord..help!

  1. #1
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    circle/tangent/chord..help!

    In the figure AT is a tangent to the circle at A. TRP and AQ are parallel chords. AP and RQ intersect at C. If <ATP = 40, <APT=45, calculate
    i) <ART
    ii) <ACR.

    i managed to get i) done...-

    <RAT=<APR=45 ->[By alternate segment theorem]
    Hence <ART= 180-(<ATR+<RAT)->[Sum of <s in △=180]
    =180 - (40+45)
    = 95.

    Plz proceed after this to find <ACR....
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  2. #2
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    Hello snigdha
    Quote Originally Posted by snigdha View Post
    In the figure AT is a tangent to the circle at A. TRP and AQ are parallel chords. AP and RQ intersect at C. If <ATP = 40, <APT=45, calculate
    i) <ART
    ii) <ACR.

    i managed to get i) done...-

    <RAT=<APR=45 ->[By alternate segment theorem]
    Hence <ART= 180-(<ATR+<RAT)->[Sum of <s in △=180]
    =180 - (40+45)
    = 95.

    Plz proceed after this to find <ACR....
    \angle PAQ = \angle RPA (alternate angles)

    \angle PAQ = \angle PRQ (same segment)

    Now look at the angles in \triangle CPR.

    Grandad
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