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Contests
National and Regional Contests
Lithuania Contests
Lithuania Team Selection Test
2006 Lithuania Team Selection Test
3
3
Part of
2006 Lithuania Team Selection Test
Problems
(1)
Four triangles of equal area
Source: Lithuanian TST 2006
4/21/2006
Inside a convex quadrilateral
A
B
C
D
ABCD
A
BC
D
there is a point
P
P
P
such that the triangles
P
A
B
,
P
B
C
,
P
C
D
,
P
D
A
PAB, PBC, PCD, PDA
P
A
B
,
PBC
,
PC
D
,
P
D
A
have equal areas. Prove that the area of
A
B
C
D
ABCD
A
BC
D
is bisected by one of the diagonals.
geometry
geometry unsolved