Question

PQ and RQ are chords of a circle equidistant from the centre.Prove that the diameter passing through Q is the bisector of angle PQR

Answer 1

Figure of this question is attached!!

Proof clearly
OP = OR (equal radii)
OQ = OQ (common)
PQ = RQ (equal chords)
OPQ =congruent= ORQ (by SSS)
∠PQO = ∠RQO (CPCT)
Therefore,
Q is the bisector of angle PQR

Answer 2

IN Δ POQ and ROQ
PQ =RQ 
OQ = OQ
OP = OR
⇒ΔPOQ = ΔROQ

by CPCT ∠PQO =∠ RQO