MathDB
Problems
Contests
International Contests
IMO Shortlist
2015 IMO Shortlist
G4
G4
Part of
2015 IMO Shortlist
Problems
(1)
Find all possible values of BT/BM
Source: 2015 ISL G4
7/7/2016
Let
A
B
C
ABC
A
BC
be an acute triangle and let
M
M
M
be the midpoint of
A
C
AC
A
C
. A circle
ω
\omega
ω
passing through
B
B
B
and
M
M
M
meets the sides
A
B
AB
A
B
and
B
C
BC
BC
at points
P
P
P
and
Q
Q
Q
respectively. Let
T
T
T
be the point such that
B
P
T
Q
BPTQ
BPTQ
is a parallelogram. Suppose that
T
T
T
lies on the circumcircle of
A
B
C
ABC
A
BC
. Determine all possible values of
B
T
B
M
\frac{BT}{BM}
BM
BT
.
geometry