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Serbia National Math Olympiad
2019 Serbia National Math Olympiad
3
3
Part of
2019 Serbia National Math Olympiad
Problems
(1)
2019 Serbia MO Day 1 P3
Source: 2019 Serbia MO
4/7/2019
Let
k
k
k
be the circle inscribed in convex quadrilateral
A
B
C
D
ABCD
A
BC
D
. Lines
A
D
AD
A
D
and
B
C
BC
BC
meet at
P
P
P
,and circumcircles of
△
P
A
B
\triangle PAB
△
P
A
B
and
△
P
C
D
\triangle PCD
△
PC
D
meet in
X
X
X
. Prove that tangents from
X
X
X
to
k
k
k
form equal angles with lines
A
X
AX
A
X
and
C
X
CX
CX
.
geometry