In an acute-angled triangle △ABC, let the perpendicular bisectors of sides AB and AC meet at O. The perpendicular from O to side BC meets BC at D. Join OB and OC.
a. (i) Prove that OB=OC.
b. (ii) Show that OD bisects BC.
c. (iii) Prove that quadrilateral BODC is cyclic.
d. (iv) Hence, show that ∠BDC=2∠BAC.