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2019 JBMO Shortlist
G1
G1
Part of
2019 JBMO Shortlist
Problems
(1)
JBMO Shortlist 2019 G1
Source:
9/12/2020
Let
A
B
C
ABC
A
BC
be a right-angled triangle with
∠
A
=
9
0
∘
\angle A = 90^{\circ}
∠
A
=
9
0
∘
and
∠
B
=
3
0
∘
\angle B = 30^{\circ}
∠
B
=
3
0
∘
. The perpendicular at the midpoint
M
M
M
of
B
C
BC
BC
meets the bisector
B
K
BK
B
K
of the angle
B
B
B
at the point
E
E
E
. The perpendicular bisector of
E
K
EK
E
K
meets
A
B
AB
A
B
at
D
D
D
. Prove that
K
D
KD
KD
is perpendicular to
D
E
DE
D
E
.Proposed by Greece
geometry