In the figure (i) given below, chords AB and CD of a circle intersect at E.

(i) Prove that triangles ADE and CBE are similar.

(ii) Given DC = 12 cm, DE = 4 cm and AE = 16 cm, calculate the length of BE.

In figure (i) given below, P is the point of intersection of the chords BC and AQ such that AB = AP. Prove that CP = CQ.

In the figure (ii) given below, AB = AC = CD, ∠ADC = 38°. Calculate

(i) ∠ABC

(ii) ∠BEC.