MathDB

3

Part of 2001 Chile National Olympiad

Problems(1)

3/2} \le /d_a/h_a + d_b/h_b/ + d_c/ h_c, angle bisectors Chile 2001 L2 P3

Source:

5/30/2019
In a triangle △ABC \vartriangle ABC , let ha,hb h_a, h_b and hc h_c the atlitudes. Let D D be the point where the inner bisector of ∠BAC \angle BAC cuts to the side BC BC and da d_a is the distance from the D D point next to AB AB . The distances db d_b and dc d_c are similarly defined. Show that: 32≤daha+dbhb+dchc \dfrac {3} {2} \le \dfrac {d_a} {h_a} + \dfrac {d_b} {h_b} + \dfrac {d_c} {h_c} For what kind of triangles does the equality hold?
geometrygeometric inequalityangle bisectordistance