MathDB
Problems
Contests
International Contests
Benelux
2017 Benelux
3
3
Part of
2017 Benelux
Problems
(1)
Another perpendicularity
Source: Benelux Mathematical Olympiad 2017, Problem 3
5/6/2017
In the convex quadrilateral
A
B
C
D
ABCD
A
BC
D
we have
∠
B
=
∠
C
\angle B = \angle C
∠
B
=
∠
C
and
∠
D
=
9
0
∘
.
\angle D = 90^{\circ}.
∠
D
=
9
0
∘
.
Suppose that
∣
A
B
∣
=
2
∣
C
D
∣
.
|AB| = 2|CD|.
∣
A
B
∣
=
2∣
C
D
∣.
Prove that the angle bisector of
∠
A
C
B
\angle ACB
∠
A
CB
is perpendicular to
C
D
.
CD.
C
D
.
geometry
Benelux