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Problems
Contests
National and Regional Contests
Saudi Arabia Contests
Saudi Arabia Pre-TST + Training Tests
2013 Saudi Arabia Pre-TST
4.4
4.4
Part of
2013 Saudi Arabia Pre-TST
Problems
(1)
lines AE,BD are perpendicular iff AB = AC
Source: 2013 Saudi Arabia Pre-TST 4.4
9/13/2020
△
A
B
C
\vartriangle ABC
△
A
BC
is a triangle,
M
M
M
the midpoint of
B
C
,
D
BC, D
BC
,
D
the projection of
M
M
M
on
A
C
AC
A
C
and
E
E
E
the midppoint of
M
D
MD
M
D
. Prove that the lines
A
E
,
B
D
AE,BD
A
E
,
B
D
are orthogonal if and only if
A
B
=
A
C
AB = AC
A
B
=
A
C
.
geometry
perpendicular
isosceles