MathDB
Problems
Contests
National and Regional Contests
Iran Contests
Iran RMM TST
2020 Iran RMM TST
4
4
Part of
2020 Iran RMM TST
Problems
(1)
Trapezoid And Segment
Source: Iranian RMM TST Day2 P4
1/14/2020
In a trapezoid
A
B
C
D
ABCD
A
BC
D
with
A
D
AD
A
D
parallel to
B
C
BC
BC
points
E
,
F
E, F
E
,
F
are on sides
A
B
,
C
D
AB, CD
A
B
,
C
D
respectively.
A
1
,
C
1
A_1, C_1
A
1
,
C
1
are on
A
D
,
B
C
AD,BC
A
D
,
BC
such that
A
1
,
E
,
F
,
A
A_1, E, F, A
A
1
,
E
,
F
,
A
lie on a circle and so do
C
1
,
E
,
F
,
C
C_1, E, F, C
C
1
,
E
,
F
,
C
. Prove that lines
A
1
C
1
,
B
D
,
E
F
A_1C_1, BD, EF
A
1
C
1
,
B
D
,
EF
are concurrent.
geometry
moving points