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Math Help - part two of the hard question trigiolgy

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    part two of the hard question trigiolgy

    A is a fixed pt on a given circle; AP , AQ are variable chords such that AP.AQ is constant. Prove that PQ touches a fixed circle, centre A
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    Quote Originally Posted by calculus_jy View Post
    A is a fixed pt on a given circle; AP , AQ are variable chords such that AP.AQ is constant. Prove that PQ touches a fixed circle, centre A
    Hello,

    unfortunately I can't give you a proof of this statement.

    I've sketched a few different situations and obviously the statement seems to be true. With the drawing (see attachment) I choose:

    R = 6 cm
    |AP| \cdot |AQ| = 48. Then I got the radius of the circle with centre A is 4 cm long. Probably there exists the "rule"(?):

    r = \frac{|AP| \cdot |AQ|}{2R}
    Attached Thumbnails Attached Thumbnails part two of the hard question trigiolgy-sehnensatzbeweis.gif  
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