In given figure, hexagon \(ABCDEF\) is circumscribed about a circle. Verify that the sum of the lengths of alternate sides is equal.
\(i.e., AB + CD + EF = BC + DE + FA\)
\(i.e., AB + CD + EF = BC + DE + FA\)
Proof:
The length of tangents drawn from a external point to a circle are equal.
\(AM=\) - - - (i)
\(BM=\) - - - (ii)
\(CN=\) - - - (iii)
\(DO=\) - - - (iv)
\(EP=\) - - - (v)
\(FQ=\) - - - (vi)
Adding (i) and (ii), we get
\(AB=\)
Adding (iii) and (iv), we get
\(CD=\)
Adding (v) and (vi), we get
\(EF=\)
Adding all these , we get
\(AB+CD+EF=BC + DE + FA\)
Hence proved.