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Problems
Contests
National and Regional Contests
Spain Contests
pOMA and PErA mathematical olympiads
2024 PErA
P4
P4
Part of
2024 PErA
Problems
(1)
Simple angle chase
Source: PErA 2024/4
3/4/2024
Let
A
B
C
ABC
A
BC
be a triangle, and let
E
E
E
,
F
F
F
be the feet of the altitudes from
B
B
B
and
C
C
C
to sides
A
C
AC
A
C
and
A
B
AB
A
B
, respectively. Let
P
P
P
and
Q
Q
Q
be the intersections of
E
F
EF
EF
with the tangents from
B
B
B
and
C
C
C
to
(
A
B
C
)
(ABC)
(
A
BC
)
, respectively. If
M
M
M
is the midpoint of
B
C
BC
BC
, prove that
(
P
Q
M
)
(PQM)
(
PQM
)
is tangent to
B
C
BC
BC
at
M
M
M
.
geometry