Question

PQ AND PR ARE EQUAL CHORDS OF A CIRCLE DRAWN ON OPPOSITE SIDES OF A DIAMETER PS.PROVE THAT ARC QS=ARC PS AND PS IS THE BISECTOR OF ANGLE QPR

Answer 1

is it to prove that qs =rs instead of ps
let o be the centre
in triangle pqo &pro
pq=pr
po=po
qo=ro
so both triangle are congruent so
< qpo=< rpo
so < qps=< rps
so ps is bisector of qpr
arc pqs=prs ,semicircle
arc pq=arc pr ,equal chord make equal arc
pq+qs=pr+rs
so qs=rs