Question

State true or false.
The incircle of an isosceles triangle 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.