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Austrian MO Beginners' Competition
2011 Austria Beginners' Competition
4
4
Part of
2011 Austria Beginners' Competition
Problems
(1)
AE=BF wanted, projections of point on circumcircle of isosceles ABC
Source: Austria Beginners' Competition 2011 p4
10/3/2021
Let
A
B
C
ABC
A
BC
be an isosceles triangle with
A
C
=
B
C
AC = BC
A
C
=
BC
. On the arc
C
A
CA
C
A
of its circumcircle, which does not contain
B
B
B
, there is a point
P
P
P
. The projection of
C
C
C
on the line
A
P
AP
A
P
is denoted by
E
E
E
, the projection of
C
C
C
on the line
B
P
BP
BP
is denoted by
F
F
F
. Prove that the lines
A
E
AE
A
E
and
B
F
BF
BF
have equal lengths.(W. Janous, WRG Ursulincn, Innsbruck)
geometry
isosceles