Question

P.Q. R and Sare points on the circumference
of a circle, centre O.PR is a diameter of the circle.
Angle PSQ = 56degree.
(a)Find the size of angle PQR.Give a reason for your
answer.

(b)Find the size of angle PRQ.Give a reason for your
answer.

(c) Find the size of angle POQ.Give a reason for your
answer.​

Answer 1

Given:

• $\angle PSQ = 56^{\circ}$

a

$\angle PQR = 90^{\circ}$ [ Angle formed by the diameter on semi-circle is 90° ( Refer to NCERT book for this theorem ) ]

b

$\angle PRQ = \angle PSQ$ [ Angles on the same segment are equal ]

$\therefore \angle PRQ = 56^{\circ}$ [ $\angle PSQ = 90^{\circ}$ , given ]

c

$\angle POQ = 90^{\circ}$ [ Line passing through the center is perpendicular on a chord and bisects the chord ]