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Byju's Answer
Standard X
Mathematics
Distance between Two Points Using Pythagoras Theorem
ABC is a tria...
Question
A
B
C
is a triangle right-angled at
B
and
D
is a point on
B
C
produced
(
B
D
>
B
C
)
,
such that
B
D
=
2
D
C
. Which one of the following is correct
?
A
A
C
2
=
A
D
2
−
3
C
D
2
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B
A
C
2
=
A
D
2
−
2
C
D
2
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C
A
C
2
=
A
D
2
−
4
C
D
2
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D
A
C
2
=
A
D
2
−
5
C
D
2
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Solution
The correct option is
A
A
C
2
=
A
D
2
−
3
C
D
2
Given,
B
D
=
2
D
C
⇒
B
C
+
C
D
=
2
D
C
⇒
B
C
=
D
C
In
△
A
B
C
, applying pythagoras theorem
A
C
2
=
A
B
2
+
B
C
2
....(i)
In
△
A
B
D
, appying pythagoras theorem
A
D
2
=
A
B
2
+
B
D
2
.....(ii)
Subtracting equations (i) and (ii), we have
A
C
2
−
A
D
2
=
B
C
2
−
B
D
2
⇒
A
C
2
−
A
D
2
=
C
D
2
−
(
2
C
D
)
2
=
C
D
2
−
4
C
D
2
=
−
3
C
D
2
⇒
A
C
2
=
A
D
2
−
3
C
D
2
Suggest Corrections
0
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In triangle
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B
C
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