Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Problem
Problem
Let
A
B
C
ABC
A
B
C
be a
Δ
\Delta
Δ
with altitudes
h
1
,
h
2
,
h
3
h_1, h_2, h_3
h
1
,
h
2
,
h
3
and inradius
r
r
r
. Prove that
h
1
+
r
h
1
−
r
+
h
2
+
r
h
2
−
r
+
h
3
+
r
h
3
−
r
≥
6
\frac{h_1 + r}{h_1 - r} + \frac{h_2 + r}{h_2 - r} + \frac{h_3 + r}{h_3 - r} \ge 6
h
1
−
r
h
1
+
r
+
h
2
−
r
h
2
+
r
+
h
3
−
r
h
3
+
r
≥
6
.
Browse the problem library