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2010 PUMaC Geometry A3: ratio with angle bisector
2010 PUMaC Geometry A3: ratio with angle bisector
Source:
August 21, 2011
geometry
ratio
angle bisector
Problem Statement
Triangle
A
B
C
ABC
A
BC
has
A
B
=
4
AB = 4
A
B
=
4
,
A
C
=
5
AC = 5
A
C
=
5
, and
B
C
=
6
BC = 6
BC
=
6
. An angle bisector is drawn from angle
A
A
A
, and meets
B
C
BC
BC
at
M
M
M
. What is the nearest integer to
100
A
M
C
M
100 \frac{AM}{CM}
100
CM
A
M
?
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