Question

If the bisector of an angle of a triangle bisects the opposite side, then the triangle is
(a) scalene
(b) equilateral
(c) isosceles
(d) right-angled

Answer 1

(c) isosceles

Let AD be the angle bisector of angle A in triangle ABC.
Applying angle bisector theorem, we get:
$\frac{AB}{AC}=\frac{BD}{DC}$

It is given that AD bisects BC.
Therefore, BD = DC
$$\begin{gathered} \Rightarrow \frac{AB}{AC}=1 \\ \Rightarrow AB=AC \end{gathered}$$

Therefore, the triangle is isosceles.