2) O is the centre of the circle. AB and AC are tangents drawn from A and B BA 1 CA prove that BACO is a square.
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Answer:
Given:
O
is the centre. Now,
∠
B
A
C
=
90
∘
A
B
=
A
C
(Tangents drawn from a point onto the circle will be equal in length)
O
B
=
O
C
(radius)
∠
A
B
O
=
∠
A
C
O
=
90
∘
(radius is perpendicular to the tangent at the point of contact)
O
B
∥
A
C
(Two lines perpendicular to the same line are parallel to each other).
A
B
=
O
C
(The distance between two parallel lines in a direction perpendicular to both the lines is constant)
⇒
A
B
=
A
C
=
O
C
=
O
B
All sides are equal in length
All angles measure
90
∘
Hence it is a square.
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