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Byju's Answer
Standard X
Mathematics
Chord Properties of Circles
In the follow...
Question
In the following figure
∠
A
B
C
=
90
∘
and
B
D
⊥
A
C
. If
A
D
=
8
c
m
,
C
D
=
2
c
m
, then the length of
B
D
is:
A
4
c
m
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B
8
c
m
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C
16
c
m
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D
10
c
m
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Solution
The correct option is
A
4
c
m
Given that:
∠
A
B
C
=
90
∘
,
B
D
⊥
A
C
,
A
D
=
8
c
m
,
C
D
=
2
c
m
To find:
B
D
=
?
Solution:
In
△
A
B
C
,
A
C
=
A
D
+
D
C
=
8
c
m
+
2
c
m
=
10
c
m
By Pythagorean theorem,
A
B
2
+
B
C
2
=
A
C
2
or,
A
B
2
+
B
C
2
=
(
10
)
2
c
m
2
or,
A
B
2
+
B
C
2
=
100
c
m
2
.
.
.
.
.
.
.
.
.
.
.
.
.
.
(
i
)
In
△
A
D
B
,
By Pythagorean theorem,
A
D
2
+
B
D
2
=
A
B
2
or,
(
8
c
m
)
2
+
B
D
2
=
A
B
2
or,
64
c
m
2
+
B
D
2
=
A
B
2
.
.
.
.
.
.
.
.
.
.
.
.
.
.
(
i
i
)
In
△
B
D
C
,
By Pythagorean theorem,
C
D
2
+
B
D
2
=
B
C
2
or,
(
2
c
m
)
2
+
B
D
2
=
B
C
2
or,
4
c
m
2
+
B
D
2
=
B
C
2
.
.
.
.
.
.
.
.
.
.
.
.
.
.
(
i
i
i
)
From eqn.(i),(ii) and (iii) we get,
64
c
m
2
+
B
D
2
+
4
c
m
2
+
B
D
2
=
100
c
m
2
or,
68
c
m
2
+
2
B
D
2
=
100
c
m
2
or,
2
B
D
2
=
100
c
m
2
−
68
c
m
2
or,
2
B
D
2
=
32
c
m
2
or,
B
D
2
=
16
c
m
2
or,
B
D
=
4
c
m
Therefore,
A
is the correct option.
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Similar questions
Q.
In the given figure, ∠ABC = 90° and BD ⊥ AC. If BD = 8 cm, AD = 4 cm, find CD.