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Rioplatense Mathematical Olympiad, Level 3
1993 Rioplatense Mathematical Olympiad, Level 3
6
6
Part of
1993 Rioplatense Mathematical Olympiad, Level 3
Problems
(1)
right triangle wanted, related to pentagon ABCDE with AE = ED, BC = CD
Source: Rioplatense 1993 L3 P6
5/26/2019
Let
A
B
C
D
E
ABCDE
A
BC
D
E
be pentagon such that
A
E
=
E
D
AE = ED
A
E
=
E
D
and
B
C
=
C
D
BC = CD
BC
=
C
D
. It is known that
∠
B
A
E
+
∠
E
D
C
+
∠
C
B
A
=
36
0
o
\angle BAE + \angle EDC + \angle CB A = 360^o
∠
B
A
E
+
∠
E
D
C
+
∠
CB
A
=
36
0
o
and that
P
P
P
is the midpoint of
A
B
AB
A
B
. Show that the triangle
E
C
P
ECP
ECP
is right.
right triangle
geometry
pentagon
equal segments
angles