MathDB
Problems
Contests
National and Regional Contests
Argentina Contests
Argentina National Olympiad
2006 Argentina National Olympiad
2
2
Part of
2006 Argentina National Olympiad
Problems
(1)
AB/BC wanted, MD_|_BD, angle bisector, midpoint related
Source: 2006 Argentina OMA L3 p2
6/16/2020
In triangle
A
B
C
,
M
ABC, M
A
BC
,
M
is the midpoint of
A
B
AB
A
B
and
D
D
D
the foot of the bisector of angle
∠
A
B
C
\angle ABC
∠
A
BC
. If
M
D
MD
M
D
and
B
D
BD
B
D
are known to be perpendicular, calculate
A
B
B
C
\frac{AB}{BC}
BC
A
B
.
geometry
angle bisector
perpendicular
ratio