Triangle Circle (Posted on 2004-11-20)

	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
	simpler yet	Steven Lord	2021-04-10 19:29:57
	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