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National and Regional Contests
Italy Contests
ITAMO
1986 ITAMO
1
1
Part of
1986 ITAMO
Problems
(1)
intersecting circles given, segment parallel to given tangent wanted
Source: ITAMO 1986 p1
2/2/2020
Two circles
α
\alpha
α
and
β
\beta
β
intersect at points
P
P
P
and
Q
Q
Q
. The lines connecting a point
R
R
R
on
β
\beta
β
with
P
P
P
and
Q
Q
Q
intersect
α
\alpha
α
again at
S
S
S
and
T
T
T
respectively. Prove that
S
T
ST
ST
is parallel to the line tangent to
β
\beta
β
at
R
R
R
.
parallel
circles
tangent
geometry