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Moscow Mathematical Olympiad
1952 Moscow Mathematical Olympiad
223
223
Part of
1952 Moscow Mathematical Olympiad
Problems
(1)
MMO 223 Moscow MO 1952 tangent incircles wanted when AB + CD = BC + AD
Source:
8/8/2019
In a convex quadrilateral
A
B
C
D
ABCD
A
BC
D
, let
A
B
+
C
D
=
B
C
+
A
D
AB + CD = BC + AD
A
B
+
C
D
=
BC
+
A
D
. Prove that the circle inscribed in
A
B
C
ABC
A
BC
is tangent to the circle inscribed in
A
C
D
ACD
A
C
D
.
geometry
incircle
tangent circles