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Byju's Answer
Standard IX
Mathematics
Chord Theorem 2
Question 8 Th...
Question
Question 8
The area of the square that can be inscribed in a circle of radius 8 cm is
(A)
256
c
m
2
(B)
128
c
m
2
(C)
64
√
2
c
m
2
(D)
64
c
m
2
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Solution
Given radius of circle r = OC = 8cm
∴
Diameter of the circle
=
A
C
=
2
×
O
C
=
2
×
8
=
16
c
m
which is equal to the diagonal of a square.
Let side of square be x
In right angled
Δ
A
B
C
,
A
C
2
=
A
B
2
+
B
C
2
[By Pythagoras theorem]
⇒
(
16
)
2
=
x
2
+
x
2
⇒
256
=
2
x
2
⇒
x
2
=
128
∴
Area of square
=
x
2
=
128
c
m
2
Alternate method
Radius of circle (r) = 8cm
Diamter of circle (d)
=
2
r
=
2
×
8
=
16
c
m
Since square inscribed in circle,
∴
Diagonal of the square = Diameter of circle
Now, Area of square
=
(
D
i
a
g
o
n
a
l
)
2
2
=
(
16
)
2
2
=
256
2
=
128
c
m
2
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Similar questions
Q.
Question 8
The area of the square that can be inscribed in a circle of radius 8 cm is
(A)
256
c
m
2
(B)
128
c
m
2
(C)
64
√
2
c
m
2
(D)
64
c
m
2
Q.
The area of the square that can be inscribed in a circle of radius 8 cm is ___________.
Q.
Find the area of a square that can be inscribed in a circle of radius
8
c
m
.
Q.
Question 7
The area of the circle that can be inscribed in a square of side 6 cm is
(A)
36
π
c
m
2
(B)
18
π
c
m
2
(C)
12
π
c
m
2
(D)
9
π
c
m
2
Q.
The maximum area of a square that can be inscribed in a circle of radius r is
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