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MathLinks Contest 6th
3.2
3.2
Part of
MathLinks Contest 6th
Problems
(1)
0632 geometry with tangential quadr. 6th edition Round 3 p2
Source:
5/3/2021
Let
A
B
C
D
ABCD
A
BC
D
be a convex quadrilateral, and the points
A
1
∈
(
C
D
)
A_1 \in (CD)
A
1
∈
(
C
D
)
,
A
2
∈
(
B
C
)
A_2 \in (BC)
A
2
∈
(
BC
)
,
C
1
∈
(
A
B
)
C_1 \in (AB)
C
1
∈
(
A
B
)
,
C
2
∈
(
A
D
)
C_2 \in (AD)
C
2
∈
(
A
D
)
. Let
M
,
N
M, N
M
,
N
be the intersection points between the lines
A
A
2
,
C
C
1
AA_2, CC_1
A
A
2
,
C
C
1
and
A
A
1
,
C
C
2
AA_1, CC_2
A
A
1
,
C
C
2
respectively. Prove that if three of the quadrilaterals
A
B
C
D
ABCD
A
BC
D
,
A
2
B
C
1
M
A_2BC_1M
A
2
B
C
1
M
,
A
M
C
N
AMCN
A
MCN
,
A
1
N
C
2
D
A_1NC_2D
A
1
N
C
2
D
are circumscriptive (i.e. there exists an incircle tangent to all the sides of the quadrilateral) then the forth quadrilateral is also circumscriptive.
geometry
6th edition