Here ABCDEF is a hexagon which circumscribe a circle.
Since the tangents drawn from a point to the circle are equal in length.
therefore AM = AR,
BM = BN,
CN = CO,
DO = DP,
EP = EQ,
FQ = FR.
now from these equations we have,
AM + BM = AR + BN⇒AB = AR + BN
CO + DO = CN + DP⇒CD = CN + DP
EQ + FQ = EP + FR⇒EF = EP + FR
now on addition these three equation gives
AB + CD + EF = AR + (BN + CN) + (DP + EP) + FR = BC + DE + FA
hence proved.
