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Byju's Answer
Standard IX
Mathematics
Chords Equidistant from Center Are Equal
Suppose two c...
Question
Suppose two chords of a circle are equidistant from the centre of the circle. Prove that the chords have equal length.
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Solution
In the figure,
O
is the center of the circle.
A
B
and
C
D
are the chords of a
circle which are equidistant from the center i.e
O
P
=
O
Q
.
To prove:
A
B
=
C
D
Proof: In triangles
P
B
O
and
Q
D
O
∠
B
P
O
=
∠
D
Q
O
=
90
0
P
O
=
Q
O
(data)
O
B
=
O
D
(radil)
P
B
O
=
Q
D
O
(RHS)
P
B
=
D
Q
Therefore,
A
B
=
C
D
Hence, the chords have equal length.
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Prove that equal chords of a circle are equidistant from the centre.