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Points and lie on a circle
MATHEMATICS · Single correct · CBSE · Mathematics · Circles · Circles
Problem
Points
A
,
B
,
P
,
A, B, P,
A
,
B
,
P
,
and
Q
Q
Q
lie on a circle.
A
B
AB
A
B
is a chord and points
P
P
P
and
Q
Q
Q
are on the same segment of
A
B
AB
A
B
. Which one of the following is always true? (a)
∠
A
P
B
+
∠
A
Q
B
=
180
∘
\angle APB + \angle AQB = 180^{\circ}
∠
A
P
B
+
∠
A
QB
=
18
0
∘
(b)
∠
A
B
P
=
∠
A
Q
B
\angle ABP = \angle AQB
∠
A
B
P
=
∠
A
QB
(c)
∠
A
P
B
=
∠
A
Q
B
\angle APB = \angle AQB
∠
A
P
B
=
∠
A
QB
(d)
∠
A
P
B
+
∠
A
Q
B
=
90
∘
\angle APB + \angle AQB = 90^{\circ}
∠
A
P
B
+
∠
A
QB
=
9
0
∘
Related theory
Circles
Circle angle properties
Angle subtended by a chord
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