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Nordic
2007 Nordic
4
Nordic MC 2007 Q4
Nordic MC 2007 Q4
Source:
March 3, 2013
ratio
geometry
geometry unsolved
Problem Statement
A line through
A
A
A
intersects a circle at points
B
,
C
B,C
B
,
C
with
B
B
B
between
A
,
C
A,C
A
,
C
. The two tangents from
A
A
A
intersect the circle at
S
,
T
S,T
S
,
T
.
S
T
ST
ST
and
A
C
AC
A
C
intersect at
P
P
P
. Show that
A
P
P
C
=
2
A
B
B
C
\frac{AP}{PC}=2\frac{AB}{BC}
PC
A
P
=
2
BC
A
B
.
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