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UPSC CDS Math Circle Questions
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© examsnet.com
Question : 46
Total: 46
In a triangle ABC, AB = BC = CA. The ratio of the radius of the circumcircle to that of the incircle is
[2014 CDS-I]
2 :1
3 :1
3 :2
None of the above
Validate
Solution:
In right ΔOBD, ∠OBD = 30°
Also,
B
D
=
C
D
=
x
2
units
Remember: Perpendicular from the centre to the chord bisects the chord
tan
30
∘
=
O
D
B
D
⇒
1
√
3
=
O
D
(
x
2
)
⇒
O
D
=
x
2
√
3
Also,
cos
30
°
=
B
D
O
B
⇒
√
3
2
=
(
x
2
)
O
B
⇒
O
B
=
x
√
3
∴
Radius of circumcircle
Radius of incircle
=
O
B
O
D
=
(
x
√
3
)
(
x
2
√
3
)
=
2
Thus, the ratio of the radius of circumcircle to that of the incircle is 2 : 1.
© examsnet.com
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