Question

O is the centre of large circle. Show that QS=QR.
The diagram is attached below.

Answer 1

not sure, thats all the info given

Answer 2

oh i see now
if you move PR so it goes through center, it shows that both QR and QS are same length as radius

Answer 3

produce the line QS to the circumference of the of circle centre 0.

Join XR .... Join PS... so you have 2 triangles... in the large circle...



you now have 2 triangles.... RQX and PQS

you need to prove congruency

start with angle XQR = angle PQS ( vertically opposite)
XR = PS ( equal chords subtend angles).... I think that is the statement
Angle XRQ = Angle PSQ ( equal angles subtended on the arc PX)

I think this proves congruency by Angle Angle Side test... so therefore QR = QS corresponding sides in congruent triangles..

Check my proof as its ages since I did circle geometry