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Indonesia Regional MO OSP SMA - geometry
2006.1
2006.1
Part of
Indonesia Regional MO OSP SMA - geometry
Problems
(1)
perpendicular inside a right triangle, altitude and midpoints
Source: 2006 Indonedia MO Province P2 q1 OSP
12/11/2020
Suppose triangle
A
B
C
ABC
A
BC
is right-angled at
B
B
B
. The altitude from
B
B
B
intersects the side
A
C
AC
A
C
at point
D
D
D
. If points
E
E
E
and
F
F
F
are the midpoints of
B
D
BD
B
D
and
C
D
CD
C
D
, prove that
A
E
⊥
B
F
AE \perp BF
A
E
⊥
BF
.
geometry
perpendicular
right triangle