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Broken Hypotenuse (Posted on 2005-02-28) Difficulty: 3 of 5
Consider a right triangle with an inscribed circle. Let x and y be the lengths of the two line segments formed on the hypotenuse by the point of tangency with the circle. What interesting fact can you prove about x*y?

See The Solution Submitted by owl    
Rating: 3.6000 (5 votes)

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Solution re: A possible solution Comment 10 of 10 |
(In reply to A possible solution by Old Original Oskar!)

Using some analytical geometry produces R=AB.AC/(AB+AC+BC), so XY works out to AB.AC/2, the area of the triangle.
  Posted by Federico Kereki on 2005-03-02 10:46:28

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