Question

State true or false.
The incircle of an isosceles $\Delta ABC$, with $AB=AC$, touches the sides $AB,BC,CA$ at $D,E$ and $F$ respectively. Then $E$ bisects $BC$.

• A. True
• B. False

Answer 1

The correct option is A True

We know that the tangents drawn from an external point to a circle are equal.

$\therefore AD=AF,$ . . . (i) [tangents from A]

$BD=BE,$ . . . (ii) [tangents from B]

$CE=CF$ . . . (iii) [tangents from C]

Now, $AB=AC$ [given]

$\Rightarrow AD+BD=AF+CF$

$\Rightarrow BD=CF$

$\Rightarrow BE=CE$ [using (ii) and (iii)]

$\Rightarrow E$ bisects $BC$.