Properties of circles(F.4)

http://flic.kr/p/j8K6GJ


(a) Prove that BD=CD
(b) Express ∠BID in terms of α and β
(c) Express ∠IBD in terms of α and β. Hence, show that BD=ID.

(d) Suppose ∠BAC= 60

i. Find ∠BOC
ii. Show that B,O,I,C are concyclic.
iii. A rectangular coordinate system is introduced in the figure so that the
coordinates of O and D are (0,0) and (0,-2) respectively.
Find the equation of the circle BOIC.

我唔識做(d) ii & (d)iii.
PLS HELP AND DETAIL.
THX