4

Part of 1962 Poland - Second Round

Problems(1)

a < b < c => d_a > d_b > d_c.

Source: Polish MO Second Round 1962 p4

Prove that if the sides

a

b

c

of a triangle satisfy the inequality

a < b < c

then the angle bisectors

d_a

d_b

d_c

of opposite angles satisfy the inequality

d_a > d_b > d_c.

inequalitiesgeometryGeometric Inequalitiesangle bisector