MathDB
Problems
Contests
National and Regional Contests
Switzerland Contests
Swiss NMO - geometry
2013.3
2013.3
Part of
Swiss NMO - geometry
Problems
(1)
BC = DE - BE if <ADC =< DBA, A projection of A on BD , cyclic ABCD
Source: Switzerland - Swiss MO 2013 p3
7/16/2020
Let
A
B
C
D
ABCD
A
BC
D
be a cyclic quadrilateral with
∠
A
D
C
=
∠
D
B
A
\angle ADC = \angle DBA
∠
A
D
C
=
∠
D
B
A
. Furthermore, let
E
E
E
be the projection of
A
A
A
on
B
D
BD
B
D
. Show that
B
C
=
D
E
−
B
E
BC = DE - BE
BC
=
D
E
−
BE
.
geometry
projection
equal angles