MathDB
Problems
Contests
National and Regional Contests
Malaysia Contests
JOM
JOM 2015
2
2
Part of
JOM 2015
Problems
(1)
AB + CD = BC
Source: Junior Olympiad of Malaysia Shortlist 2015 G5 (JOM P2)
7/17/2015
Let
A
B
C
D
ABCD
A
BC
D
be a convex quadrilateral. Let angle bisectors of
∠
B
\angle B
∠
B
and
∠
C
\angle C
∠
C
intersect at
E
E
E
. Let
A
B
AB
A
B
intersect
C
D
CD
C
D
at
F
F
F
. Prove that if
A
B
+
C
D
=
B
C
AB+CD=BC
A
B
+
C
D
=
BC
, then
A
,
D
,
E
,
F
A,D,E,F
A
,
D
,
E
,
F
is cyclic.
geometry