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UPSC CDS Math Circle Questions
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© examsnet.com
Question : 20
Total: 46
Two parallel chords of a circle whose diameter is 13 cm are respectively 5 cm and 12 cm in length. If both the chords are on the same side of the diameter, then the distance between these chords is
[2017 CDS-I]
5.5 cm
5 cm
3.5 cm
3 cm
Validate
Solution:
Remember :
The perpendicular drawn from the centre of the circle to the chord bisects the chord.
Now, OE ⊥ A
⇒
A
E
=
B
E
=
A
B
2
=
5
2
cm
Also,OD ⊥ CD
⇒
C
F
=
D
F
=
C
D
2
=
6
c
m
O
A
=
O
C
=
13
2
c
m
(Radius of the circle)
In right ΔOCF,
O
F
=
√
O
C
2
−
C
F
2
=
√
(
13
2
)
2
−
6
2
=
√
25
4
=
5
2
c
m
In right ΔOAE
O
E
=
√
O
A
2
−
A
E
2
=
√
(
13
2
)
2
−
(
5
2
)
2
=
√
144
4
=
6
c
m
Therefore, distance between the chords
=
O
E
−
O
F
=
6
−
5
2
=
3.5
c
m
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