MathDB
Problems
Contests
National and Regional Contests
Vietnam Contests
Hanoi Open Mathematics Competition
2016 Hanoi Open Mathematics Competitions
10
10
Part of
2016 Hanoi Open Mathematics Competitions
Problems
(1)
h_a + 4h_b + 9h_c > 36r, altitudes (HOMC 2016 Junior Q10)
Source:
7/20/2019
Let
h
a
,
h
b
,
h
c
h_a, h_b, h_c
h
a
,
h
b
,
h
c
and
r
r
r
be the lengths of altitudes and radius of the inscribed circle of
△
A
B
C
\vartriangle ABC
△
A
BC
, respectively. Prove that
h
a
+
4
h
b
+
9
h
c
>
36
r
h_a + 4h_b + 9h_c > 36r
h
a
+
4
h
b
+
9
h
c
>
36
r
.
geometry
inequalities
geometric inequality