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In the given figure, D, E and F are the ...

In the given figure, D, E and F are the points where the incircle of the `Delta`ABC touches F the sides BC, CA and AB respectively. Show that AF+ BD + CE = AE + BF + CD = (perimeter of `Delta ABC`)

Text Solution

Verified by Experts

We know, length of tangents from any common point outside a circle are always equal.
`:. AF = AE ->(1)`
`BD = BF->(2)`
`CE = CD ->(3)`
Adding (1),(2) and (3),
`AF+BD+CE = AE+BF+CD`
Now, perimeter of `ABC = AB+BC+AC`
`=AF+BF+BD+DC+CE+AE`
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