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.
(i) Prove that OB=OC.
(ii) Show that OD bisects BC.
(iii) Prove that quadrilateral BODC is cyclic.
(iv) Hence, show that ∠BDC=2∠BAC.