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Which of the following correctly states the relation between a central angle and an…
MATHEMATICS · Single correct · CBSE · Mathematics · Circles · Circles
Problem
Which of the following correctly states the relation between a central angle
∠
A
O
B
\angle AOB
∠
A
O
B
and an inscribed angle
∠
A
C
B
\angle ACB
∠
A
C
B
that subtend the same arc
A
B
AB
A
B
of a circle with centre
O
O
O
? (a)
∠
A
O
B
=
1
2
∠
A
C
B
\angle AOB = \dfrac{1}{2}\angle ACB
∠
A
O
B
=
2
1
∠
A
C
B
(b)
∠
A
O
B
+
∠
A
C
B
=
180
∘
\angle AOB + \angle ACB = 180^\circ
∠
A
O
B
+
∠
A
C
B
=
18
0
∘
(c)
∠
A
O
B
=
2
∠
A
C
B
\angle AOB = 2\angle ACB
∠
A
O
B
=
2∠
A
C
B
(d)
∠
A
O
B
=
∠
A
C
B
\angle AOB = \angle ACB
∠
A
O
B
=
∠
A
C
B
Related theory
Circles
Circle angle properties
Angle subtended by a chord
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