Question

Two interior angle bisectors of a triangle meet at a point O. Without any other information, can we say that the point O is the incentre of the triangle? Answer in Yes/No.

Answer 1

$\underset{–}{\text{Given:}}$ Two interior angle bisectors of a triangle meet at the point $O$.

$\text{Incentre}$ is the point where all the three interior angle bisectors of a triangle meet.


$\therefore$ All the interior angle bisectors will meet at a single point.

If any two of the three interior angle bisectors of a triangle meet at a point $O$, then the third interior angle bisector must meet at the same point which is the incentre of the triangle.

Hence, the given point $O$ is the incentre of the triangle.