We know that two circles will be congruent if they have equal radii
From the figure we know that if the two chords are equal then the corresponding arcs are congruent
We know that PQ is the common chord in both the circles
So their corresponding arcs are equal
It can be written as
Arc PCQ = arc PDQ
We know that the congruent arcs have the same degree
So we get
∠QAP = ∠QBP
We know that the base angles of isosceles triangle are equal
So we get
QA = QB
Therefore, it is proved that QA = QB.