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Contests
National and Regional Contests
India Contests
Regional Mathematical Olympiad
1995 India Regional Mathematical Olympiad
1
Perpendicularity
Perpendicularity
Source: Indian RMO 1995 Problem 1
October 26, 2005
exterior angle
Problem Statement
In triangle
A
B
C
ABC
A
BC
,
K
K
K
and
L
L
L
are points on the side
B
C
BC
BC
(
K
K
K
being closer to
B
B
B
than
L
L
L
) such that
B
C
⋅
K
L
=
B
K
⋅
C
L
BC \cdot KL = BK \cdot CL
BC
⋅
K
L
=
B
K
⋅
C
L
and
A
L
AL
A
L
bisects
∠
K
A
C
\angle KAC
∠
K
A
C
. Show that
A
L
⊥
A
B
.
AL \perp AB.
A
L
⊥
A
B
.
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