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In a circle with centre
MATHEMATICS · Multi-part · CBSE · Mathematics · Circles · Circles
Problem
In a circle with centre
O
O
O
, quadrilateral
A
B
C
D
ABCD
A
B
C
D
is inscribed. It is given that
∠
A
O
B
=
∠
C
O
D
\angle AOB = \angle COD
∠
A
O
B
=
∠
C
O
D
and
∠
B
O
C
=
70
∘
\angle BOC = 70^\circ
∠
B
O
C
=
7
0
∘
. (i) Prove that
A
B
=
C
D
AB = CD
A
B
=
C
D
. (ii) If
∠
A
O
B
=
110
∘
\angle AOB = 110^\circ
∠
A
O
B
=
11
0
∘
, find the value of
∠
A
D
C
\angle ADC
∠
A
D
C
. (iii) If the length of
A
B
AB
A
B
is
8.4
cm
8.4\,\text{cm}
8.4
cm
, determine the length of
C
D
CD
C
D
with justification.
Related theory
Circles
Chord Properties
Equal chords and their distances
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