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Problems
Contests
National and Regional Contests
India Contests
India National Olympiad
1991 India National Olympiad
5
5
Part of
1991 India National Olympiad
Problems
(1)
Find the angle
Source: INMO 1991 Problem 5
10/3/2005
Triangle
A
B
C
ABC
A
BC
has an incenter
I
I
I
. Let points
X
X
X
,
Y
Y
Y
be located on the line segments
A
B
AB
A
B
,
A
C
AC
A
C
respectively, so that
B
X
⋅
A
B
=
I
B
2
BX \cdot AB = IB^2
BX
⋅
A
B
=
I
B
2
and
C
Y
⋅
A
C
=
I
C
2
CY \cdot AC = IC^2
C
Y
⋅
A
C
=
I
C
2
. Given that the points
X
,
I
,
Y
X, I, Y
X
,
I
,
Y
lie on a straight line, find the possible values of the measure of angle
A
A
A
.
geometry
incenter