Wednesday, July 22, 2009

Problem 816. Tangential or Circumscribed Quadrilateral: Pitot Theorem

Geometry Problem
Click the figure below to see the complete Tangential or Circumscribed Quadrilateral: Pitot Theorem.

 Tangential or Circumscribed Quadrilateral: Pitot Theorem.
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Tangential or Circumscribed Quadrilateral: Pitot Theorem
Level: High School, SAT Prep, College geometry

10 comments:

  1. it is easy to prove using th fact that tangents from the same point to the same circle are equal

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  2. Anonymous is right... by substitution we have a reflexive property so the theorem is true. Quite elementary

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  3. if the the point of contacts are joined and perimeter of this cyclic quad is given , can we find the perimeter of the circumscribed quad.?

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  4. The converse is more difficult to prove.

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    Replies
    1. The converse may not necessary true.

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    2. Can anyone tell me the proof of the converse

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  5. Replies
    1. To Jacob: It was published in 2009 as "Pitot Theorem" now is the problems collection as problem 816 for more solutions. Thanks.

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  6. Problem 816
    If AB ,BC,CD and DA intersects the tangent circle in K,L,M and N respectively, then AK=AN, BK=BL,CL=CM,DM=DN.But AB+CD=AK+KB+CM+DM=AN+(BL+CL)+DN=BC+AD.
    APOSTOLIS MANOLOUDIS 4 HIGH SHCOOL OF KORYDALLOS PIRAEUS GREECE

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