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Problems
Contests
National and Regional Contests
Switzerland Contests
Switzerland Team Selection Test
2001 Switzerland Team Selection Test
7
7
Part of
2001 Switzerland Team Selection Test
Problems
(1)
perpendicular wanted , where O is circumcenter
Source: Switzerland - Swiss TST 2001 p7
2/18/2020
Let
A
B
C
ABC
A
BC
be an acute-angled triangle with circumcenter
O
O
O
. The circle
S
S
S
through
A
,
B
A,B
A
,
B
, and
O
O
O
intersects
A
C
AC
A
C
and
B
C
BC
BC
again at points
P
P
P
and
Q
Q
Q
respectively. Prove that
C
O
⊥
P
Q
CO \perp PQ
CO
⊥
PQ
.
geometry
Circumcenter
perpendicular