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Silk Road
2018 Silk Road
1
1
Part of
2018 Silk Road
Problems
(1)
silk road 2018 geometry
Source: SRMC 2018 P1
8/30/2018
In an acute-angled triangle
A
B
C
ABC
A
BC
on the sides
A
B
AB
A
B
,
B
C
BC
BC
,
A
C
AC
A
C
the points
H
H
H
,
L
L
L
,
K
K
K
so that
C
H
⊥
A
B
CH \perp AB
C
H
⊥
A
B
,
H
L
∥
A
C
HL \parallel AC
H
L
∥
A
C
,
H
K
∥
B
C
HK \parallel BC
HK
∥
BC
. Let
P
P
P
and
Q
Q
Q
feet of altitudes of a triangle
H
B
L
HBL
H
B
L
, drawn from the vertices
H
H
H
and
B
B
B
respectively. Prove that the feet of the altitudes of the triangle
A
K
H
AKH
A
KH
, drawn from the vertices
A
A
A
and
H
H
H
lie on the line
P
Q
PQ
PQ
.
geometry
altitudes