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Problems
Contests
National and Regional Contests
Mexico Contests
Mexico National Olympiad
1999 Mexico National Olympiad
5
5
Part of
1999 Mexico National Olympiad
Problems
(1)
length of segment of intersections of pairs of external angle bisectors = s
Source: Mexican Mathematical Olympiad 1999 OMM P5
7/28/2018
In a quadrilateral
A
B
C
D
ABCD
A
BC
D
with
A
B
/
/
C
D
AB // CD
A
B
//
C
D
, the external bisectors of the angles at
B
B
B
and
C
C
C
meet at
P
P
P
, while the external bisectors of the angles at
A
A
A
and
D
D
D
meet at
Q
Q
Q
. Prove that the length of
P
Q
PQ
PQ
equals the semiperimeter of
A
B
C
D
ABCD
A
BC
D
.
geometry
Angle Bisectors