Ratio of Radii (Posted on 2008-03-27)

    r     a sin(A)
   --- ≤ ----------
    R        2s

	Submitted by Bractals
Rating: 3.5000 (2 votes)
Solution:	(Hide)
Look at triangle ABC. Since /A ≥ 90°, A must lie on or inside the circle with BC as a diameter. Therefore, ha, the altitude on BC, is less than or equal to a/2. ha ≤ a/2 ==> aha ≤ a2/2 ==> 2rs ≤ a2/2 ==> r ≤ [a/2s][a/2] ==> r ≤ [a/2s][R sin(A)] r a sin(A) ==> --- ≤ ---------- R 2s

	Subject	Author	Date
	A useful intermediate!	Chesca Ciprian	2008-03-27 16:32:22