In △ABC, let D be the midpoint of AB and E be the midpoint of AC. Through D draw a line perpendicular to AB, and through E draw a line perpendicular to AC. These two perpendicular lines meet at O.
a. (i) Prove that △ODA≅△ODB.
b. (ii) Prove that △OEA≅△OEC.
c. (iii) Using the above, show that OB=OC and hence justify that O is equidistant from B and C.