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UPSC CDS Math Circle Questions
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© examsnet.com
Question : 5
Total: 46
Two equal circles intersect such that each passes through the centre of the other. If the length of the common chord of the circles is 10
√
3
cm, then what is the diameter of the circle ?
[2019 CDS-I]
10 cm
15 cm
20 cm
30 cm
Validate
Solution:
Given common chord CD
=
10
√
3
cm
Let the radius of each circle be 2x.
Then AB = 2x and AE = x
C
E
=
10
√
3
2
=
5
√
3
m
In ΔAEC:
A
C
2
=
A
E
2
+
C
E
2
⇒
(
2
x
)
2
=
x
2
+
(
5
√
3
)
2
⇒
3
x
2
=
75
⇒
x
=
5
cm
Diameter of a circle
=
4
x
=
4
×
5
=
20
c
m
.
© examsnet.com
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