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2016 LMT
18
18
Part of
2016 LMT
Problems
(1)
2016 LMT Individual #18
Source:
4/10/2016
Let
△
A
B
C
\triangle ABC
△
A
BC
be a triangle with
A
B
=
5
,
B
C
=
6
,
C
A
=
7
AB=5, BC=6, CA=7
A
B
=
5
,
BC
=
6
,
C
A
=
7
. Suppose
P
P
P
is a point inside
△
A
B
C
\triangle ABC
△
A
BC
such that
△
B
P
A
∼
△
A
P
C
\triangle BPA\sim \triangle APC
△
BP
A
∼
△
A
PC
. If
A
P
AP
A
P
intersects
B
C
BC
BC
at
X
X
X
, find
B
X
C
X
\frac{BX}{CX}
CX
BX
.Proposed by Nathan Ramesh