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VTRMC
2006 VTRMC
Problem 6
Problem 6
Part of
2006 VTRMC
Problems
(1)
triangle inside another, bisectors
Source: VTRMC 2006 P6
6/5/2021
In the diagram below,
B
P
BP
BP
bisects
∠
A
B
C
\angle ABC
∠
A
BC
,
C
P
CP
CP
bisects
∠
B
C
A
\angle BCA
∠
BC
A
, and
P
Q
PQ
PQ
is perpendicular to
B
C
BC
BC
. If
B
Q
⋅
Q
C
=
2
P
Q
2
BQ\cdot QC=2PQ^2
BQ
⋅
QC
=
2
P
Q
2
, prove that
A
B
+
A
C
=
3
B
C
AB+AC=3BC
A
B
+
A
C
=
3
BC
. https://services.artofproblemsolving.com/download.php?id=YXR0YWNobWVudHMvOC8zL2IwZjNjMDAxNWEwMTc1ZGNjMTkwZmZlZmJlMGRlOGRhYjk4NzczLnBuZw==&rn=VlRSTUMgMjAwNi5wbmc=
geometry
Triangles