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Durer Math Competition
Durer Math Competition CD 1st Round - geometry
2016.C1
2016.C1
Part of
Durer Math Competition CD 1st Round - geometry
Problems
(1)
2 points and 3 projections concyclic 2015-16 Dürer Round1 C1 D1
Source:
12/5/2022
Let
P
P
P
be an arbitrary point of the side line
A
B
AB
A
B
of the triangle
A
B
C
ABC
A
BC
. Mark the perpendicular projection of
P
P
P
on the side lines
A
C
AC
A
C
and
B
C
BC
BC
as
A
1
A_1
A
1
and
B
1
B_1
B
1
respectively. Denote
C
1
C_1
C
1
he foot of the alttiude starting from
C
C
C
. Prove that the points
A
1
A_1
A
1
,
B
1
B_1
B
1
,
C
1
C_1
C
1
,
C
C
C
and
P
P
P
lie on a circle.
geometry
Concyclic
Durer