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2020 USOJMO
2
2
Part of
2020 USOJMO
Problems
(1)
apparently circles have two intersections :'(
Source: 2020 USOJMO Problem 2
6/21/2020
Let
ω
\omega
ω
be the incircle of a fixed equilateral triangle
A
B
C
ABC
A
BC
. Let
ℓ
\ell
ℓ
be a variable line that is tangent to
ω
\omega
ω
and meets the interior of segments
B
C
BC
BC
and
C
A
CA
C
A
at points
P
P
P
and
Q
Q
Q
, respectively. A point
R
R
R
is chosen such that
P
R
=
P
A
PR = PA
PR
=
P
A
and
Q
R
=
Q
B
QR = QB
QR
=
QB
. Find all possible locations of the point
R
R
R
, over all choices of
ℓ
\ell
ℓ
.Proposed by Titu Andreescu and Waldemar Pompe
USA(J)MO
geometry