In a triangle ABC if r1=2r2=3r3 the a/2 is
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Answer:
Also given
r
1
=
2
r
2
=
3
r
3
So
r
1
r
2
=
2
⇒
s
−
b
s
−
a
=
2
⇒
s
−
b
=
2
s
−
2
a
⇒
s
+
b
−
2
a
=
0
⇒
2
s
+
2
b
−
4
a
=
0
⇒
a
+
b
+
c
+
2
b
−
4
a
=
0
⇒
c
+
3
b
−
3
a
=
0
⇒
c
=
3
a
−
3
b
Again
r
1
r
3
=
3
⇒
s
−
c
s
−
a
=
3
⇒
(
s
−
c
)
=
3
(
s
−
a
)
=
3
s
−
3
a
⇒
(
s
−
c
)
=
3
s
−
3
a
⇒
2
s
+
c
−
3
a
=
0
⇒
a
+
b
+
c
+
c
−
3
a
=
0
⇒
b
+
2
c
−
2
a
=
0
Inserting
c
=
3
a
−
3
b
we gat
⇒
b
+
2
(
3
a
−
3
b
)
−
2
a
=
0
⇒
b
+
6
a
−
6
b
−
2
a
=
0
⇒
4
a
−
5
b
=
0
⇒
4
a
=
5
b
⇒
a
:
b
=
5
:
4
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