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Problems
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International Contests
IMO Longlists
1978 IMO Longlists
21
21
Part of
1978 IMO Longlists
Problems
(1)
Proving a tangency with square, incircle and parallels.
Source:
10/28/2010
A circle touches the sides
A
B
,
B
C
,
C
D
,
D
A
AB,BC, CD,DA
A
B
,
BC
,
C
D
,
D
A
of a square at points
K
,
L
,
M
,
N
K,L,M,N
K
,
L
,
M
,
N
respectively, and
B
U
,
K
V
BU, KV
B
U
,
K
V
are parallel lines such that
U
U
U
is on
D
M
DM
D
M
and
V
V
V
on
D
N
DN
D
N
. Prove that
U
V
UV
U
V
touches the circle.
geometry
analytic geometry
geometry unsolved