Question

In figure if AB=AC , prove that BE=EC.​

Answer 1

Answer:

Since tangents from an exterior point to a circle are equal

in length.

AD=AF[Tangents from A]−−−−(i)

BD=BE[Tangents from B]−−−−(ii)

CE=CF[Tangents from C]−−−−(iii)

Now,

AB=AC [Given]

⇒AB−AD=AC−AD [ Subtracting AD from both sides ]

⇒AB−AD=AC−AF [ using (i) ]

⇒BD=CF

⇒BE=CF [ using (ii) ]

⇒BE=CE [ using (iii) ]

Answer 2

Answer:

Since tangents from an exterior point to a circle are equal

in length.

AD=AF[Tangents from A]−−−−(i)

BD=BE[Tangents from B]−−−−(ii)

CE=CF[Tangents from C]−−−−(iii)

Now,

AB=AC [Given]

⇒AB−AD=AC−AD [ Subtracting AD from both sides ]

⇒AB−AD=AC−AF [ using (i) ]

⇒BD=CF

⇒BE=CF [ using (ii) ]

⇒BE=CE [ using (iii) ]

Hence Proved