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Byju's Answer
Standard VII
Mathematics
Radii, Chord, Diameter and Circumference of the Circle
Two concentri...
Question
Two concentric circles are of radii
5
c
m
and
3
c
m
. Find the length of the chord of the larger circle which touches the smaller circle.
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Solution
Let
O
be the common center of two concentric circles and let
A
B
be a chord of larger circle touching the smaller circle at
P
join
O
P
Since
O
P
is the radius of the smaller circle to any chrod of the circle bisects the chord.
∴
A
P
=
B
P
In right
Δ
A
P
O
we have
O
A
2
=
A
P
2
+
O
P
2
⇒
25
−
9
=
A
P
2
⇒
A
P
2
=
16
⇒
A
P
=
4
Now
A
B
=
2
,
A
P
=
2
×
4
=
8
[
∵
A
P
=
P
B
]
hence the length of the chord of the larger circle which touches the smaller circle is
8
c
m
.
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Q.
Two concentric circles are of radii 5 cm and 3 cm, respectively. Find the length of the chord of the larger circle that touches the smaller circle.