Question

IF HEXAGON ABCDEF CIRCUMSCRIBE A CIRCLE PROVE THAT AB+CD+EF=BC+DE+FA.

Answer 1

Here ABCDEF is a hexagon which circumscribe a circle. 

Since the tangents are equal in length 

So AM = AR,  

BM = BN,  

CN = CO,  

DO = DP, 

EP = EQ, 

FQ = FR, 

From the above equations we will get 

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