- #1

ER901

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## Homework Statement

Let t_i be the lengths of the line segments that bisect angle Ai of a triangle. The segments go from A_i to the opposite side. Let a_i be the lengths of the sides opposite angle A_i. Prove the following inequalities:

[tex]\sum[/tex]from i=1to 3 1/t[tex]_{}i[/tex] > [tex]\sum[/tex] from i=1 to 3 1/a[tex]_{}i[/tex]

[tex]\sum[/tex]from i=1 to 3 t[tex]_{}i[/tex] < [tex]\sum[/tex] from i=1 to 3 a[tex]_{}i[/tex]

## The Attempt at a Solution

I'm not sure where to start.. but this is what I have in mind:

a_2, a_3 > t_1 ; a_1, a_3 > t_2 and so on...

but then I don't know what to do next

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