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CAT 2016 Quantitative Ability
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© examsnet.com
Question : 24
Total: 34
A square is inscribed in a circle and the circle is inscribed in a regular octagon. Find the ratio of the area of the square to that of the octagon
(
1
+
√
2
)
:
4
(
2
√
2
−
1
)
:
4
(
√
2
−
1
)
:
4
Cannot be determined
Validate
Solution:
Let the length of the side of the octagon and the radius of the circle be ‘a’ units and T’ units respectively. Therefore, the length of the side of the square will be
(
2
r
√
2
)
units.
LM= LA+AB+BM
⇒
2
r
=
a
√
2
+
a
+
a
√
2
⇒
r
=
a
(
1
+
√
2
)
2
Hence, the ratio
=
(
2
r
√
2
)
2
8
×
1
2
×
r
×
a
=
r
2
a
=
a
(
1
+
√
2
2
)
2
a
=
(
1
+
√
2
)
:
4
© examsnet.com
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