Question

solve it. based on chapter circles.

Answer 1

in triangles POS and ROQ..
....angle P = angle Q. (alternate interior angles)
....OS = OR...(1)
(PQ is bisector).
...angle POS = TOQ.. ..vertically oppo. angles..
hence /\ POS= /\ ROQ
OP = OQ (C.P.C.T)...(2)
now
PQ is diameter..
OP = OQ
it means that O is the centre..
now O is centre this means that ... OS=OR=radius of circle
OS+ OR = RS...
OS + OS= RS...(OS=OR)
2 (OS) = RS
2 (radius of circle)= RS
diameter = RS...
(2 (radius)= Diameter)