Two tangents AB and AC drawn from an external point A of a circle touch the circle at the point B and C .A tangent drawn a point X lies on minor are BC intersects AB and AC at the points D and E respectively. Prove that perimeter of `DeltaADE=2AB.`

Explanation

Let AB and AC are two tangents ddrawn from an external point A to the circle with centre O at the points B and C respectively.
`therefore AB =AC……..(1)`
Similarly, `DB=Dxand EX=EC…..(2)`
Now, perimeter of `DeltaADE=AD+ DE+EA`
`=AD+(DX+EX)+ EA` [as per figure]
`+AD +(DB+EC)+EA` [from (2)]
`=(AD+DB)+ (AE+EC)`
`=AB+AC` [as per figure]
`AB+AB[becauseAC=AB]=2AB.`
Hence permeter of `DeltaADE=2AB.` (Proved)