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Byju's Answer
Standard X
Mathematics
Similar Triangles
If r1, r2, r3...
Question
If
r
1
,
r
2
,
r
3
represent the exradius and r represents the in radius then,
1
r
1
+
1
r
2
+
1
r
3
−
1
r
= 0
A
True
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B
False
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Solution
The correct option is
A
True
r
1
=
Δ
s
−
a
a
n
d
r
=
Δ
s
1
r
1
+
1
r
2
+
1
r
3
−
1
r
=
s
−
a
Δ
+
s
−
b
Δ
+
s
−
c
Δ
−
s
Δ
=
3
s
−
(
a
+
b
+
c
)
Δ
−
s
Δ
=
3
s
−
(
2
s
)
−
s
Δ
=
3
s
−
3
s
Δ
=
0
∴
Given statement is true
Suggest Corrections
0
Similar questions
Q.
If
r
1
,
r
2
,
r
3
represent the exradii and r represents the inradius then,
1
r
1
+
1
r
2
+
1
r
3
−
1
r
= 0
Q.
If
r
1
,
r
2
,
r
3
represent the exradii and r represents the inradius then,
1
r
1
+
1
r
2
+
1
r
3
−
1
r
= 0
Q.
Prove that :
a
(
r
r
1
+
r
2
r
3
)
=
b
(
r
r
2
+
r
3
r
1
)
=
c
(
r
r
3
+
r
1
r
2
)
where
r
is inradius and
r
1
,
r
2
,
r
3
are exradius of triangle
A
B
C
and
a
,
b
,
c
are the corresponding sides.
Q.
Assertion :In a
△
A
B
C
, if
a
<
b
<
c
and
r
is inradius and
r
1
,
r
2
,
r
3
are the axradii opposite to angle
A
,
B
,
C
respectively, then
r
<
r
1
<
r
2
<
r
3
Reason:
△
A
B
C
,
r
1
r
2
+
r
2
r
3
+
r
3
r
1
=
r
1
r
2
r
3
r
Q.
Prove
1
r
1
+
1
r
2
+
1
r
3
−
1
r
=
0
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