Two equal circles intersect in `P` and `Q` . A straight line through `P` meets the circles in `A` and `B` . Prove that `Q A=Q Bdot`

Explanation

As we know that the two circles will congruent if they have equal radii.

Also, we know that if two chords are equal then the corresponding arcs are congruent.

Since, PQ is the common chord in both the circles.

So their corresponding arcs are equal.

arc PCQ=arc PDQ

Now, the congruent arcs have the same degree

`angleQAP=angleQBP`

`therefore` the base angles of an isosceles triangle are equal

...