Question

Take a line segment PQ and a point R not on the line containing PQ. Join PR and QR
(see Fig. 10.10). Then Z PRQ is called the angle subtended by the line segment PQ
at the point R. What are angles POQ, PRQ and PSQ called in Fig. 10.11? Z POQ is
the angle subtended by the chord PQ at the centre 0, Z PRQ and Z PSQ are
respectively the angles subtended by PQ at points R and S on the major and minor
arcs PQ
R
R
P
P
S​

Answer 1

Answer:

Given POQ is the Diameter of a circle.

Angle subtended by diameter on circumference is 90

∘

∠PRQ=90

∘

and side PR=QR so, ∠RPQ=∠RQP [Isosceles traingle PRQ]

Sum of all three angle of triangle is 180

∘

Therefore ∠PRQ+∠RQP+∠RPQ=180

∘

90

∘

+∠RQP+∠RPQ=180

∘

90

∘

+2∠RPQ=180

∘

[∠RPQ=∠RQP]

∠RPQ=

2

90

∘

∠RPQ=45

∘

Therefore option D is the answer.