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Arc of a circle subtends two inscribed angles and at distinct points and on the circle
MATHEMATICS · Single correct · CBSE · Mathematics · Circles · Circles
Problem
Arc
P
Q
PQ
P
Q
of a circle subtends two inscribed angles
∠
P
R
Q
\angle PRQ
∠
P
R
Q
and
∠
P
S
Q
\angle PSQ
∠
P
S
Q
at distinct points
R
R
R
and
S
S
S
on the circle. Which of the following must always be true? (a)
∠
P
R
Q
+
∠
P
S
Q
=
180
∘
\angle PRQ + \angle PSQ = 180^{\circ}
∠
P
R
Q
+
∠
P
S
Q
=
18
0
∘
(b)
∠
P
R
Q
=
∠
P
O
Q
\angle PRQ = \angle POQ
∠
P
R
Q
=
∠
P
O
Q
(c)
∠
P
R
Q
=
∠
P
S
Q
\angle PRQ = \angle PSQ
∠
P
R
Q
=
∠
P
S
Q
(d)
∠
P
R
Q
>
∠
P
S
Q
\angle PRQ > \angle PSQ
∠
P
R
Q
>
∠
P
S
Q
Related theory
Circles
Circle angle properties
Angle subtended by a chord
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