Five congruent circles, with centres C, D, F, G and H, are arranged so that each centre lies on the circumference of at least two other circles, as shown in the attachment below.
a) Let P be the intersection point of line segments AI and BJ. Prove that angle APB is 60 degrees and hence that P lies on the circle with centre C.
b) The line segment EF and circle with centre C intersect at F; let Q be their second point of intersection. Prove that Q also lies on the circle with centre P which passes through C.
I'm really stuck on problem b); I tried using chords AB and PQ and the cyclic quadrilateral ABPQ to show that PCQ is an equilateral triangle and, thus, to prove that Q lies on the circle with centre P. However, I realised that my proof led to a dead end... How would I solve this question?
Any help would be extremely appreciated!