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(i) OA2+OB2+OC2-OD2-OE2-OF2=AF2+BD2+CE2,
(ii) AF2+BD2+CE2=AE2+CD2+BF2
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: Join OA, OB, and OC
(i) Applying Pythagoras theorem in ΔAOF, we obtain
OA2 = OF2 + AF2
Similarly, in ΔBOD,
OB2 = OD2 + BD2
Similarly, in ΔCOE,
OC2 = OE2 + EC2
Adding these equations, we get
OA2 + OB2 + OC2 = OF2 + AF2 + OD2 + BD2 + OE2 + EC2
OA2 + OB2 + OC2 – OD2 – OE2 – OF2 = AF2 + BD2 + EC2
(ii) From the above given result,
AF2 + BD2 + EC2 = (AO2 – OE2) + (OC2 – OD2) + (OB2 – OF2)
Therefore,
AF2 + BD2 + EC2 = AE2 + CD2 + BF2
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