I can do part (i) it is just equiangular...
But I can't do the rest
If I try I might get them but I am so tired right now and this is the last question in the paper !
CP/CM=AE/AM
angle C = angle A.
therefore they are similar 2 sides in the same ratio and their included angle is equal.
might add some more as i get em
iii) angle OFB=90 (midpoint of a chord forms a right angle with the origin)
angle OMP = angle OMQ = angle QEX (simirarry)
therefore they are cyclic quads as opposite angles are supplementary