MathDB
Problems
Contests
National and Regional Contests
India Contests
India National Olympiad
2017 India National Olympiad
5
5
Part of
2017 India National Olympiad
Problems
(1)
AI perpendicular to PQ and AI=PQ
Source: INMO Problem 5
1/15/2017
Let
A
B
C
ABC
A
BC
be a triangle with
∠
A
=
9
0
∘
\angle{A}=90^{\circ}
∠
A
=
9
0
∘
and
A
B
<
A
C
AB<AC
A
B
<
A
C
. Let
A
D
AD
A
D
be the altitude from
A
A
A
on to
B
C
BC
BC
, Let
P
,
Q
P,Q
P
,
Q
and
I
I
I
denote respectively the incentres of triangle
A
B
D
,
A
C
D
ABD,ACD
A
B
D
,
A
C
D
and
A
B
C
ABC
A
BC
. Prove that
A
I
AI
A
I
is perpendicular to
P
Q
PQ
PQ
and
A
I
=
P
Q
AI=PQ
A
I
=
PQ
.
geometry