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Byju's Answer
Standard X
Mathematics
Theorem of Internal and External Division of Chords
If a, b, c ar...
Question
If a, b, c are in A.P., then the following are also in A.P.
1
b
c
,
1
c
a
,
1
a
b
.
A
True
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B
False
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Solution
The correct option is
A
True
We have,
a
,
b
,
c
are in
A
.
P
On dividing by
a
b
c
, we get
a
a
b
c
,
b
a
b
c
,
c
a
b
c
are also in
A
.
P
1
b
c
,
1
c
a
,
1
a
b
are also in
A
.
P
Hence, this is the answer.
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Similar questions
Q.
If a, b, c are in A.P., then
1
b
c
,
1
c
a
,
1
a
b
are in
Q.
If
a
,
b
,
c
are in A.P. then prove that
1
b
c
,
1
c
a
,
1
a
b
are also in A.P
Q.
If
1
a
,
1
b
,
1
c
are in A.P., prove that
(i)
bc,ca,ab are in A.P.
(ii) a(b+c), b(c+a), c(a+b) are in A.P
Q.
1
a
,
1
b
and
1
c
are in A.P. Show that: bc, ca and ab are also in A.P.
Q.
If a,b,c are in A.P. then
a
+
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c
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+
1
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are in
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