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UPSC CDS Math Circle Questions
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© examsnet.com
Question : 40
Total: 46
The chord of an arc of a circle is of length x, the height of the arc is y and the radius of the circle is z. Which one of the following is correct?
[2014 CDS-II]
y
(
2
z
−
y
)
=
x
2
y
(
2
z
−
y
)
=
4
x
2
2
y
(
2
z
−
y
)
=
x
2
4
y
(
2
z
−
y
)
=
x
2
Validate
Solution:
OA = OB = OC = z, AB = x and CD = y.
OD ⊥ AB.
∴
A
D
=
B
D
=
x
2
Remember:
Perpendicular from the centre to the chord bisects the chord.
OD = OC – CD = z – y
In right ΔOAD,
z
2
=
(
x
2
)
2
+
(
z
−
y
)
2
⇒
z
2
=
x
2
4
+
z
2
+
y
2
−
2
y
z
⇒
x
2
4
=
2
y
z
−
y
2
=
y
(
2
z
−
y
)
⇒
x
2
=
4
y
(
2
z
−
y
)
© examsnet.com
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