Question

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

Answer 1

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Answer 2

Answer with explanation:

We know that the tangents drawn from any external point have same length.

---------------(1)

In the given figure we have a circle inscribed in triangle.

Using (1), we have

From point A , AD=AF      (a)

From point B , BD=BE      (b)

From point C ,  EC=CF   (c)

Given : AB=AC      (i)

Also, AB=AD+BD   and  AC= AF+CF      (ii)

From (i) and (ii)

AD+BD=AF+CF

Using (a), we get BD=CF       (iii)

From (b), (c) and (iii)

BD=BE=CF=EC

⇒BE=EC

Hence Proved.