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Standard VII
Mathematics
Question
In a square ABCD, diagonals meet at O. P is a point on BC such that OB = BP.
∠
B
O
P
=
3
∠
C
O
P
State whether the above statement is true or false.
True
False
A
False
B
True
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Solution
Verified by Toppr
The correct option is
A
True
Given,
A
B
C
D
is a
S
q
u
a
r
e
and
O
B
=
B
P
In
△
O
B
P
,
∠
B
O
P
=
∠
O
P
B
∠
O
B
P
=
90
2
=
45
∘
--------[by symmetry or diagonals bisect the angles at the vertices, in a square]
We know that, Sum of interior angles of a triangle is equal to
180
∘
∠
B
O
P
=
180
−
45
2
=
135
2
=
67.5
∘
----------(1)
∠
B
O
C
=
90
∘
--------[diagonals bisect at right angles, in a square]
∠
P
O
C
=
90
−
67.5
=
22.5
∘
-----------(11)
From (1) and (11)
∠
B
O
P
=
3
∠
P
O
C
Hence its True
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Similar Questions
Q1
In a square ABCD, diagonals meet at O. P is a point on BC such that OB = BP.
∠
B
O
P
=
3
∠
C
O
P
State whether the above statement is true or false.
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Q2
State true or false
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State true or false:
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