In the given Fig if AB=AC, then prove that (a) BE=EC - Maths - Circles

Question

In
the given Fig if AB=AC, then
prove that (a) BE=EC
(b) AB=BC
(c) BE=AD
(d) BC=AC

Priyanka Kedia · Accepted Answer

Dear Student,

We know that the tangents drawn from an exterior point to a circle are equal in length
So,AD=AF  Tangents from A      
1BD=BE  Tangents from B     
2CE=CF  Tangents from C     
3Given, AB=AC           
4Subtract AD from both sides in equation4, we get,AB-AD=AC-AD⇒AB-AD=AC-AF    Using1⇒BD=CF⇒BE=CE             Using1Similarly, BE=CF and EC=AFAdding equation1 and 2, we get,AD+BD=AF+BE⇒AD+BD=EC+BE              Using AF=EC⇒AB=BCSubtract BE from both sides in AB=BC, we get,BC-AD=AB-AD⇒BC-AF=AB-AD⇒BC-CE=AB-AD⇒EC=AD⇒BE=ADAdding equation2 and 3, we get,BD+EC=CF+BE⇒BD+EC=CF+CE⇒BE+EC=AF+CF              Using2⇒BC=AC

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In the given Fig. if AB=AC, then prove that (a) BE=EC (b) AB=BC (c) BE=AD (d) BC=AC

In the given Fig. if AB=AC, then
prove that (a) BE=EC
(b) AB=BC
(c) BE=AD
(d) BC=AC