From an initial triangle ΔA0B0C0, a sequence of triangles ΔA1B1C1, A2B2C2, ... is formed such that, at each stage, Ak+1, Bk+1 and Ck+1 are the points where the incircle of ΔAkBkCk touches the sides BkCk, CkAk and AkBk respectively.
(a) Express ∠Ak+1Bk+1Ck+1 in terms of ∠AkBkCk.
(b) Deduce that, as k increases, ∠AkBkCk tends to 60∘.