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Byju's Answer
Standard X
Mathematics
Angles in Alternate Segments
In figure, if...
Question
In figure, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to
[ 2 marks ]
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Solution
We know that, the perpendicular from the centre of a circle to a chord bisects the chord.
A
C
=
C
B
=
1
2
A
B
=
1
2
×
8
=
4
c
m
g
i
v
e
n
,
O
A
=
5
c
m
[ 1 mark ]
A
O
2
=
A
C
2
+
O
C
2
[
u
s
i
n
g
p
y
t
h
a
g
o
r
a
s
t
h
e
o
r
e
m
]
(
5
)
2
=
(
4
)
2
+
O
C
2
25
=
16
+
O
C
2
O
C
2
=
25
−
16
=
9
O
C
=
3
c
m
[taking positive square root, because length is always positive]
OA = OD [same radius of a circle]
OD = 5 cm
CD = OD - OC = 5 - 3 = 2 cm
[ 1 mark ]
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