(a) AF2 + BD2 + CE2 = AE2 + CD2 + BF2
Join OA, OB and OC.
By Pythagoras, theorem,
In ΔAOF, AF2 = AO2 – OF2 …(i)
In ΔBOD, BD2 = BO2 – OD2 …(ii)
In ΔCOE, CE2 = CO2 – OE2 …(iii)
Adding (i), (ii) and (iii), we get
AF2 + BD2 + CE2 = AO2 – OF2 + BO2 – OD2 + CO2 – OE2