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Rioplatense Mathematical Olympiad, Level 3
1997 Rioplatense Mathematical Olympiad, Level 3
4
4
Part of
1997 Rioplatense Mathematical Olympiad, Level 3
Problems
(1)
2 circles tangent internally to a third circle and to one secant of that circle
Source: Rioplatense Olympiad 1997 level 3 P4
9/4/2018
Circles
c
1
c_1
c
1
and
c
2
c_2
c
2
are tangent internally to circle
c
c
c
at points
A
A
A
and
B
B
B
, respectively, as seen in the figure. The inner tangent common to
c
1
c_1
c
1
and
c
2
c_2
c
2
touches these circles in
P
P
P
and
Q
Q
Q
, respectively. Show that the
A
P
AP
A
P
and
B
Q
BQ
BQ
lines intersect the circle
c
c
c
at diametrically opposite points. https://cdn.artofproblemsolving.com/attachments/0/a/9490a4d7ba2038e490a858b14ba21d07377c5d.gif
geometry
tangent circles