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Chord Triangle Constant (Posted on 2015-03-21) Difficulty: 4 of 5

  
Let Γ be a circle with center O and radius r. Let P be a point inside Γ
( different from O ) with |OP| = p.

a) Prove there exists a point A outside Γ such that for all chords BC
of Γ through P the quantity (b+c)/a is constant ( where a, b, and c
are the side lengths of ΔABC ).

b) What is the constant in terms of p and r?

c) Prove that the point A is unique.
  

See The Solution Submitted by Bractals    
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Comments: ( You must be logged in to post comments.)
  Subject Author Date
re: Possible SolutionBractals2015-03-25 22:18:18
SolutionPossible SolutionHarry2015-03-24 17:51:33
Some ThoughtsSines and secantsbroll2015-03-23 04:54:09
A GSP startJer2015-03-21 20:45:12
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