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2017 Serbia National Math Olympiad
3
Tangents inducing isogonals
Tangents inducing isogonals
Source: Serbian MO 2017 6
April 2, 2017
geometry
excircle
Problem Statement
Let
k
k
k
be the circumcircle of
△
A
B
C
\triangle ABC
△
A
BC
and let
k
a
k_a
k
a
be A-excircle .Let the two common tangents of
k
,
k
a
k,k_a
k
,
k
a
cut
B
C
BC
BC
in
P
,
Q
P,Q
P
,
Q
.Prove that
∡
P
A
B
=
∡
C
A
Q
\measuredangle PAB=\measuredangle CAQ
∡
P
A
B
=
∡
C
A
Q
.
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