in the given figure AB and AC are 2 tangents to a circle from an external point a DE is - Maths - Circles

Question

in the given figure AB and AC are 2 tangents to a circle from an
external point a DE is line segment touching the circle at F and
intersecting AB at D and AC at E prove that AB =1/2 the perimeter
of triangle ADE

Pooja Khanna · Accepted Answer

Dear Student,

Please follow the solution to
the above given query:
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/ck-files/ck_565b01d9410f8%20png"
style="width: 143px; height: 113px;">

Tangents drawn from an external point to the circle are equal
DB = DF … (1)
EF = EC … (2)
AB = AC … (3)

Now,
AB = AC
⇒ AD + DB = AE + EC
⇒ AD + DF = AE + EF -------- ( Using (1) and (2) )

Perimeter of âˆ† ADE = AD + DE + EA
= AD + ( DF + FE ) + EA
= (AD + DF) + (FE + EA)
= 2 ( AD + DF ) ( AD + DF = AE + EFâ€‹ )
= 2 ( AD + DB ) -------- ( Using (1) )
= 2 AB

⇒Perimeter of △ADE=2AB⇒AB=Perimeter of △ADE2
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in the given figure AB and AC are 2 tangents to a circle from an external point a DE is line segment touching the circle at F and intersecting AB at D and AC at E prove that AB =1/2 the perimeter of triangle ADE