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National and Regional Contests
India Contests
India Pre-Regional Mathematical Olympiad
2015 India PRMO
12
PRMO 2015. p12.
PRMO 2015. p12.
Source:
April 9, 2024
geometry
incircle
rectangle
Problem Statement
12.
12.
12.
In a rectangle
A
B
C
D
ABCD
A
BC
D
A
B
=
8
AB=8
A
B
=
8
and
B
C
=
20.
BC=20.
BC
=
20.
Let
P
P
P
be a point on
A
D
AD
A
D
such that
∠
B
P
C
=
9
0
o
.
\angle{BPC}=90^o.
∠
BPC
=
9
0
o
.
If
r
1
,
r
2
,
r
3
.
r_1,r_2,r_3.
r
1
,
r
2
,
r
3
.
are the radii of the incircles of triangles
A
P
B
,
APB,
A
PB
,
B
P
C
,
BPC,
BPC
,
and
C
P
D
.
CPD.
CP
D
.
what is the value of
r
1
+
r
2
+
r
3
?
r_1+r_2+r_3 ?
r
1
+
r
2
+
r
3
?
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