Geometry Problem

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Tangential or Circumscribed Quadrilateral: Pitot Theorem

Level: High School, SAT Prep, College geometry

## Wednesday, July 22, 2009

### Problem 816. Tangential or Circumscribed Quadrilateral: Pitot Theorem

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

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

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

ReplyDeleteThe converse is more difficult to prove.

ReplyDeleteThe converse may not necessary true.

DeleteCan anyone tell me the proof of the converse

DeleteProblem 816.

ReplyDeleteWhy 816 was published in 2009?

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

DeleteProblem 816

ReplyDeleteIf 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