Question

a hexagon ABCDEF circumscribe a circle .Prove that AB+ CD+ EF=BC+DE+FA​

Answer 1

Answer:

your answer is here !

Step-by-step explanation:

Solution:-

Given : Here ABCDEF is a hexagon which circumscribes a circle.

Since the tangents drawn from a point to the circle are equal in length.

Let the inside points where the circle touches the hexagon be 'M', 'N', 'O', 'P', 'Q' and 'R' respectively.

Therefore,

AM = AR ...(1)

BM = BN ...(2)

CN = CO ...(3)

DO = DP ...(4)

EP = EQ ...(5)

FQ = FR ...(6)

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 adding the above three, we get

AB + CD + EF = AR + (BN + CN) + (DP + EP) + FR = BC + DE + FA

⇒ AB + CD + EF = BC + DE + FA

Hence proved.

good morning have a nice day !

follow me !