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Byju's Answer
Standard X
Mathematics
Chord Properties of Circles
Two concentri...
Question
Two concentric circles are of radii
5
cm and
3
cm. Find the length of chord of the larger circle which touches the smaller circle.
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Solution
Let two circles have the same centre
O
and
A
B
is a chord of the larger circle touching the smaller circle at
C
.
O
A
=
5
c
m
and
O
C
=
3
c
m
Now,
As we know that the tangent at any point of a circle is perpendicular to the radius through the point of contact.
Therefore,
In
△
O
A
C
,
O
A
2
=
O
C
2
+
A
C
2
(
By pythagoras theorem
)
⇒
A
C
2
=
O
A
2
−
O
C
2
⇒
A
C
2
=
(
5
)
2
−
(
3
)
2
⇒
A
C
=
√
25
−
9
=
√
16
=
4
c
m
Since perpendicular drawn from the centre of circle bisects the chord.
Therefore,
A
B
=
2
A
C
⇒
A
B
=
2
×
4
=
8
c
m
Hence the length of the chord is
8
c
m
.
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