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India National Olympiad
1995 India National Olympiad
1
1
Part of
1995 India National Olympiad
Problems
(1)
Triangle property [A = 30° yields AT = 2 * BC]
Source: INMO 1995 Problem 1
10/6/2005
In an acute angled triangle
A
B
C
ABC
A
BC
,
∠
A
=
3
0
∘
\angle A = 30^{\circ}
∠
A
=
3
0
∘
,
H
H
H
is the orthocenter, and
M
M
M
is the midpoint of
B
C
BC
BC
. On the line
H
M
HM
H
M
, take a point
T
T
T
such that
H
M
=
M
T
HM = MT
H
M
=
MT
. Show that
A
T
=
2
B
C
AT = 2 BC
A
T
=
2
BC
.
geometry
geometric transformation
reflection
circumcircle
trigonometry
homothety
parallelogram