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Math Help - Geometry

  1. #1
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    Geometry

    PQ is diameter . Show that QC & AP bisect angle C & angle A.
    Last edited by sreesuja; February 26th 2013 at 06:31 AM. Reason: TYPING MISTAKE
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  2. #2
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    Re: Geometry

    Pl Give some information about A and C
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  3. #3
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    Re: Geometry

    ABCD is a cyclic quadrilateral.where PQ is the diameter. Show that QC and AP bisect angle C & and angle A.
    Last edited by sreesuja; February 26th 2013 at 08:04 PM. Reason: TYPING MISTAKE
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  4. #4
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    Re: Geometry

    I find stii something missing. Please see attached figureGeometry-quad.png
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  5. #5
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    Re: Geometry

    The diagram is
    Attached Thumbnails Attached Thumbnails Geometry-circle-diag.bmp  
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  6. #6
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    Re: Geometry

    Sreesuja

    the problem you mentioned is wrongly formulated.
    it must be like this .

    In a cyclic quadrilateral ABCD the angle bisector of A meets the circle at P and the angle bisector of C meets he circle at Q .Show that PQ is a diameter of the circle.
    Be carefull the converse you are doing is not correct ..not all the diameters of the circle are bisectors of the angle C or A!!!!.
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  7. #7
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    Re: Geometry

    Proof:

    Please revise your diagram also it is wrong .put in the place of A Q AND IN PLACE OF Q... A ALSO INTERCHANGE C WITH P
    THEN USE THE MAIN PROPERTY OF CYCLIC QUADRELATERALS..THAT STIPULATES : angle A + angle C =180.
    here half of angle A + half of angle C must be 90.
    Indeed look: the upper half of A has a DP as the coresponding arc. similarly the upper half of C has as coresponding arcs QA+AD
    THEREFORE ARC(QA)+ARC(AD)+ARC(DP) = 180 AND THE POINTS Q AND P LYING ON A DIAMETER.
    AS SIMPLE AS SUCH
    MINOAS
    Thanks from sreesuja
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