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 Triangle Circle (Posted on 2004-11-20)
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) πr/(h+r) __________________________________ 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).

 Subject Author Date answer K Sengupta 2007-12-23 12:12:57 Ambiguity in Problem & a Simpler Solution Steve Cotler 2004-11-23 16:05:45 r in terms of a, b, h Larry 2004-11-20 20:38:17 re(2): Solution (correction) np_rt 2004-11-20 19:41:22 re: Solution (alternate expression) owl 2004-11-20 19:40:32 re: Solution Richard 2004-11-20 19:31:22 Thoughts, a method but not the answer Larry 2004-11-20 19:04:59 Solution np_rt 2004-11-20 18:34:17

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