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Byju's Answer
Standard VIII
Mathematics
Dilations
In given figu...
Question
In given figure ABC is an isosceles triangle with AB=AC and D is a point on AC such that
B
C
2
=
A
C
×
C
D
. Prove that BD=BC.
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Solution
We have,
B
C
2
=
A
C
×
C
D
and
A
B
=
A
C
⇒
B
C
×
B
C
=
A
C
×
C
D
and
∠
B
=
∠
C
⇒
B
C
A
C
=
C
D
B
C
and
∠
B
=
∠
C
⇒
B
C
C
A
=
D
C
C
B
and
∠
B
=
∠
C
So, by SAS-criterion of similarity, we have
△
B
C
A
∼
△
D
C
B
⇒
B
C
D
C
=
C
A
C
B
=
B
A
D
B
⇒
C
A
C
B
=
B
A
D
B
⇒
B
A
C
A
=
D
B
C
B
⇒
1
=
D
B
C
B
[
∵
BA=CA]
⇒
D
B
=
C
B
⇒
B
D
=
B
C
[
H
e
n
c
e
p
r
o
v
e
d
]
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