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If ABCDEF is a regular hexagon, prove th...

If ABCDEF is a regular hexagon, prove that `AD+EB+FC=4AB`.

Text Solution

Verified by Experts

We have,
`AD+EB+FC=(AB+BC+CD)+(ED+DC+CB)+FC`
`=AB+(BC+CB)+(CD+DC)+ED+FC`

`=AB+O+O+AB+2AB=4AB`
`(becauseED=AB,FC=2AB)` hence proved.
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