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Standard X
Mathematics
Length of Arc of a Sector
Question
In given figure, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB then CD is equal to
2 cm
3 cm
4 cm
5 cm
A
4 cm
B
5 cm
C
2 cm
D
3 cm
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Solution
Verified by Toppr
OC is perpendicular on chord AB
∴
O
C
bisects the chord AB
⇒
A
C
=
C
B
Now,
A
C
+
C
B
=
A
B
⇒
A
C
+
C
B
=
8
⇒
A
C
=
8
2
⇒
4
cm
△
O
C
A
is a right angled triangle
∴
A
O
2
=
A
C
2
+
O
C
2
⇒
5
2
=
4
2
+
O
C
2
⇒
5
2
−
4
2
=
O
C
2
⇒
O
C
2
=
9
⇒
O
C
=
3
Since, OD is the radius of the circle
∴
O
A
=
O
D
=
5
cm
C
D
=
O
D
−
O
C
⇒
5
−
3
=
2
cm
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