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Bulgaria Contests
Bulgaria National Olympiad
1985 Bulgaria National Olympiad
Problem 5
Problem 5
Part of
1985 Bulgaria National Olympiad
Problems
(1)
computational of angles on media in triangle
Source: Bulgaria 1985 P5
6/16/2021
Let
P
P
P
be a point on the median
C
M
CM
CM
of a triangle
A
B
C
ABC
A
BC
with
A
C
≠
B
C
AC\ne BC
A
C
=
BC
and the acute angle
γ
\gamma
γ
at
C
C
C
, such that the bisectors of
∠
P
A
C
\angle PAC
∠
P
A
C
and
∠
P
B
C
\angle PBC
∠
PBC
intersect at a point
Q
Q
Q
on the median
C
M
CM
CM
. Determine
∠
A
P
B
\angle APB
∠
A
PB
and
∠
A
Q
B
\angle AQB
∠
A
QB
.
Triangles
geometry