MathDB
Problems
Contests
National and Regional Contests
Kyrgyzstan Contests
Kyrgyzstan National Olympiad
2010 Kyrgyzstan National Olympiad
4
4
Part of
2010 Kyrgyzstan National Olympiad
Problems
(1)
distance product(KgNM2010)
Source:
4/25/2011
Point
O
O
O
is chosen in a triangle
A
B
C
ABC
A
BC
such that
d
a
,
d
b
,
d
c
{d_a},{d_b},{d_c}
d
a
,
d
b
,
d
c
are distance from point
O
O
O
to sides
B
C
,
C
A
,
A
B
BC,CA,AB
BC
,
C
A
,
A
B
, respectively. Find position of point
O
O
O
so that product
d
a
⋅
d
b
⋅
d
c
{d_a} \cdot {d_b} \cdot {d_c}
d
a
⋅
d
b
⋅
d
c
becomes maximum.
geometry
geometry unsolved