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UPSC CDS Math Circle Questions
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© examsnet.com
Question : 4
Total: 46
In a circle of radius 8 cm, AB and AC are two chords such that AB = AC = 12 cm. What is the length of chord BC ?
[2019 CDS-I]
2
√
6
cm
3
√
6
cm
3
√
7
cm
6
√
7
cm
Validate
Solution:
In ΔOBD:
B
D
2
=
8
2
–
(
A
D
–
8
)
2
=
8
2
–
A
D
2
–
8
2
+
16
A
D
In ΔABD:
B
D
2
=
12
2
−
A
D
2
144
−
A
D
2
=
16
A
D
−
A
D
2
⇒
A
D
=
9
c
m
O
D
=
A
D
−
O
A
=
9
−
8
=
1
cm
B
D
=
√
8
2
−
1
2
=
√
63
cm
∴
B
C
=
2
B
D
=
2
√
63
=
6
√
7
c
m
© examsnet.com
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