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Triangle Circle (Posted on 2004-11-20) Difficulty: 3 of 5
Begin with a right triangle with hypotenuse h.

Inscribe a circle and label its radius, r.

What is the ratio of the area of the circle to that of the triangle?

  Submitted by SilverKnight    
Rating: 3.0000 (4 votes)
Solution: (Hide)

Let the two legs of the triangle be length x and y. We see that h=x+y-2r.

Draw three "sub-triangles" by connecting the center of the circle to the vertices of the triangle.

The area of the triangle is the sum of the areas of the 3 smaller triangles. Thus the area is xr/2+yr/2 + hr/2 = r(x+y+h)/2 = r(h+2r+h)/2 = r(h+r).

The area of the circle is πr2, so the ratio of areas is (π r2)/r(h+r) = π r/(h+r).

Comments: ( You must be logged in to post comments.)
  Subject Author Date
answerK Sengupta2007-12-23 12:12:57
SolutionAmbiguity in Problem & a Simpler SolutionSteve Cotler2004-11-23 16:05:45
Solutionr in terms of a, b, hLarry2004-11-20 20:38:17
re(2): Solution (correction)np_rt2004-11-20 19:41:22
re: Solution (alternate expression)owl2004-11-20 19:40:32
re: SolutionRichard2004-11-20 19:31:22
Some ThoughtsThoughts, a method but not the answerLarry2004-11-20 19:04:59
Solutionnp_rt2004-11-20 18:34:17
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