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Ceva theorm

  1. May 1, 2012 #1
    I have tried but still cannot get it. Simple geometry question.

    Tangents to the inscribed circle of triangle PQR are parallel to [QR], [RP] and [PQ]
    respectively and they touch the circle at A, B and C.
    Prove that [PA], [QB] and [RC] are concurrent

    relevant formula:

    Ceva's theorm (Any three concurrent lines drawn from the vertices of a triangle divide the sides (produced if necessary) so that the product of their respective ratios is unity/

    Thank you in advance!

    I have tried on geometry sketch pad. It did works.....
     
    Last edited: May 2, 2012
  2. jcsd
  3. May 5, 2012 #2

    coolul007

    User Avatar
    Gold Member

    some thoughts: The parallel lines form a triangle congruent to the first rotated 180 degrees. The tangents of both triangles have a corresponding point 180 degrees apart on the circle.
     
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