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National and Regional Contests
France Contests
France Team Selection Test
2003 France Team Selection Test
3
3
Part of
2003 France Team Selection Test
Problems
(1)
France TST 2003 D1 Q3
Source:
3/2/2013
M
M
M
is an arbitrary point inside
△
A
B
C
\triangle ABC
△
A
BC
.
A
M
AM
A
M
intersects the circumcircle of the triangle again at
A
1
A_1
A
1
. Find the points
M
M
M
that minimise
M
B
⋅
M
C
M
A
1
\frac{MB\cdot MC}{MA_1}
M
A
1
MB
⋅
MC
.
geometry
circumcircle
trigonometry
incenter
trig identities
Law of Sines
geometry unsolved