## 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.

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

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

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

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.?

4. The converse is more difficult to prove.

1. The converse may not necessary true.

2. Can anyone tell me the proof of the converse

5. Why 816 was published in 2009?

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

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