Question

Question 6
If D is a point on the side BC of a $\Delta ABC$ such that AD bisects $\angle BAC$. Then,
(A) BD = CD
(B) BA > BD
(C) BD > BA
(D) CD > CA

Answer 1

Given $\Delta ABC$ such that AD bisects $\angle BAC$
$\Rightarrow \angle BAD=\angle CAD$

In $\Delta ACD,\angle BDA$ is an exterior angle
$\therefore \angle BDA>\angle CAD...\left(i\right)$
$\Rightarrow \angle BDA>\angle BAD\left[\text{from eq.(i)}\right]$
$\Rightarrow BA>BD$ [side opposite to greater angle is greater]