MathDB
Problems
Contests
National and Regional Contests
Moldova Contests
Moldova Team Selection Test
2021 Moldova Team Selection Test
11
11
Part of
2021 Moldova Team Selection Test
Problems
(1)
Prove that the lines KH and CD are perpendicular
Source: Moldova TST 2021
9/20/2021
In a convex quadrilateral
A
B
C
D
ABCD
A
BC
D
the angles
B
A
D
BAD
B
A
D
and
B
C
D
BCD
BC
D
are equal. Points
M
M
M
and
N
N
N
lie on the sides
(
A
B
)
(AB)
(
A
B
)
and
(
B
C
)
(BC)
(
BC
)
such that the lines
M
N
MN
MN
and
A
D
AD
A
D
are parallel and
M
N
=
2
A
D
MN=2AD
MN
=
2
A
D
. The point
H
H
H
is the orthocenter of the triangle
A
B
C
ABC
A
BC
and the point
K
K
K
is the midpoint of
M
N
MN
MN
. Prove that the lines
K
H
KH
KH
and
C
D
CD
C
D
are perpendicular.
geometry