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National and Regional Contests
Serbia Contests
Serbia Team Selection Test
1980 Yugoslav Team Selection Test
Problem 1
Problem 1
Part of
1980 Yugoslav Team Selection Test
Problems
(1)
geo config of venn diagram
Source: Yugoslav TST 1980 P1
5/29/2021
Circles
k
k
k
and
l
l
l
intersect at points
P
P
P
and
Q
Q
Q
. Let
A
A
A
be an arbitrary point on
k
k
k
distinct from
P
P
P
and
Q
Q
Q
. Lines
A
P
AP
A
P
and
A
Q
AQ
A
Q
meet
l
l
l
again at
B
B
B
and
C
C
C
. Prove that the altitude from
A
A
A
in triangle
A
B
C
ABC
A
BC
passes through a point that does not depend on
A
A
A
.
geometry