MathDB
Problems
Contests
National and Regional Contests
Moldova Contests
Moldova Team Selection Test
2017 Moldova Team Selection Test
3
3
Part of
2017 Moldova Team Selection Test
Problems
(1)
P on altitude and concurrent lines
Source: Moldova TST 2017, B3
3/6/2017
Let
ω
\omega
ω
be the circumcircle of the acute nonisosceles triangle
Δ
A
B
C
\Delta ABC
Δ
A
BC
. Point
P
P
P
lies on the altitude from
A
A
A
. Let
E
E
E
and
F
F
F
be the feet of the altitudes from P to
C
A
CA
C
A
,
B
A
BA
B
A
respectively. Circumcircle of triangle
Δ
A
E
F
\Delta AEF
Δ
A
EF
intersects the circle
ω
\omega
ω
in
G
G
G
, different from
A
A
A
. Prove that the lines
G
P
GP
GP
,
B
E
BE
BE
and
C
F
CF
CF
are concurrent.
geometry