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Ecuador Mathematical Olympiad (OMEC)
2021 Ecuador NMO (OMEC)
3
3
Part of
2021 Ecuador NMO (OMEC)
Problems
(1)
Geometry, Locus and moving circumferences
Source: OMEC Ecuador National Olympiad Final Round 2021 N3 P3 day 1
11/7/2024
Let
T
1
T_1
T
1
and
T
2
T_2
T
2
internally tangent circumferences at
P
P
P
, with radius
R
R
R
and
2
R
2R
2
R
, respectively. Find the locus traced by
P
P
P
as
T
1
T_1
T
1
rolls tangentially along the entire perimeter of
T
2
T_2
T
2
geometry
perimeter
Locus
national olympiad