If a hexagon ABCDEF circumscribe a circle, prove that `AB + CD + EF=BC+DE+FA`

Explanation

Given A hexagon ABCDEF circumscirbe a circle.

To prove `AB+CD+EF=BC+DE+FA`
Proof `AB+CD+EF=(AQ+QB)+(CS+SD)+(EU+UF)`
`=AP+BR+CR+DT+ET+FP`
`=(AP+FP)+(BR+CR)+(DT+ET)`
`AB+CD+EF=AF+BC+DE` :.AQ=AP
QB=BR
CS=CR
DS=DT
EU=ET
[tangents drawn from an external point to a circle are equal]
Hence proved.