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CDS Model Paper 4 Mathematics
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© examsnet.com
Question : 61
Total: 100
Let
X
be any point within a square
A
B
C
D
.
On
A
X
a square
A
X
Y
Z
is described such that
D
is within it. Which one of the following is correct?
A
X
=
D
Z
∠
A
D
Z
=
∠
B
A
X
A
D
=
D
Z
B
X
=
D
Z
Validate
Solution:
In
Δ
A
B
X
and
Δ
A
D
Z
A
B
=
A
D
(side of square
A
B
C
D
)
and
A
X
=
A
Z
(side of square
A
X
Y
Z
)
Let
∠
B
A
X
=
θ
∴
∠
X
A
D
=
90
°
−
θ
Also,
A
X
Y
Z
is a square,
∴
∠
Z
A
X
=
90
°
⇒
∠
Z
A
D
+
∠
X
A
D
=
90
°
⇒
∠
Z
A
D
=
90
°
−
(
90
°
−
θ
)
=
θ
i.e.,
∠
B
A
X
=
∠
Z
A
D
∴
Δ
A
B
X
≌
Δ
A
D
Z
∴
B
X
=
D
Z
(by CPCT)
© examsnet.com
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