MathDB
Problems
Contests
National and Regional Contests
Albania Contests
Albania JBMO TST
2015 Albania JBMO TST
2
2
Part of
2015 Albania JBMO TST
Problems
(1)
find the measure of the angle $\angle MCN.$
Source: Albania JTST 2015
10/4/2023
The triangle
A
B
C
ABC
A
BC
has
∠
B
C
A
=
9
0
∘
.
\angle BCA=90^{\circ}.
∠
BC
A
=
9
0
∘
.
Bisector of angle
∠
C
A
B
\angle CAB
∠
C
A
B
intersects the side
B
C
BC
BC
in point
P
P
P
and bisector of angle
∠
A
B
C
\angle ABC
∠
A
BC
intersects the side
A
C
AC
A
C
in point
Q
.
Q.
Q
.
If
M
M
M
and
N
N
N
are projections of
P
P
P
and
Q
Q
Q
on side
A
B
AB
A
B
, find the measure of the angle
∠
M
C
N
.
\angle MCN.
∠
MCN
.
geometry