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Subject: "a sangaku problem"     Previous Topic | Next Topic
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Conferences The CTK Exchange High school Topic #350
Reading Topic #350
alexbadmin
Charter Member
1873 posts
Aug-12-06, 08:05 PM (EST)
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"a sangaku problem"
 
   Chords KN and ST are perpendicular to diameter CP of circle (O) at points Q and R. SQ intersects the circle in V. (K, S are on one side of CP, N and T on the other.) Let r be the radius of the circle (M) inscribed into the curvilinear triangle TQV. Prove that

1/r = 1/PQ + 1/QR.

In addition, it would be nice to have a short independent proof of the fact that r is independent of the radius of (O).


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alexbadmin
Charter Member
1873 posts
Aug-14-06, 02:55 PM (EST)
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1. "RE: a sangaku problem"
In response to message #0
 
   A solution is at

https://www.cut-the-knot.org/Curriculum/Geometry/MixtilinearLike.shtml


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