I don't think this is true.
A tiangle with semiperimter s = (a+b+c)/2 has area
A = sr
Also, picking side a as base, and its associated altitude h,
A = ah/2
Consider a triangle with sides 6,10,14. Look at the ratio h/r for the three altitudes. We want to show that h/r >= 3. But, consider the altitude based on the side a of length 14:
sr = ah/2
h/r = 2s/a = 30/14 < 3
Prove that the least height (h) of a triangle contains a circle of radius (r) is h=3r
4 answers
I used a program to draw a circle inside a triangle using height = 3 radius
and it was fit !
and it was fit !
I know there are triangles where it is true, I'm just not able to prove it is true for all triangles.
Did you draw the triangle I mentioned? If so, I must have goofed up somewhere.
What sides, radius and altitudes did you get?
Did you draw the triangle I mentioned? If so, I must have goofed up somewhere.
What sides, radius and altitudes did you get?
I just did some figuring for the 10-6-14 triangle, and
altitude to the side of 14 = 9.2857
area = 7*9.2857 = 65
65 = rs = 15r
so, r=4.33
9.2857 < 3*4.33
Check my math, but I think the problem's assertion is false.
altitude to the side of 14 = 9.2857
area = 7*9.2857 = 65
65 = rs = 15r
so, r=4.33
9.2857 < 3*4.33
Check my math, but I think the problem's assertion is false.