The bisectors of $\angle B$ and $\angle C$ of an isosceles $△ABC$ with $AB=AC$ intersect each other at a point $O$. Show that the exterior angle adjacent to $\angle ABC$ is equal to $\angle BOC.$

The image of an object placed at a point $A$ before a plane mirror $LM$ is seen at the point $B$ by an observer at $D$, as shown in the figure. Prove that the image is as far behind the mirror as the object is in front of the mirror.

In the adjoining figure, If $O$ is midpoint of $BM$, explain how one can find the breadth of the river without crossing it.

Is it possible to construct a triangle with lengths of its sides as given below? (yes/no)

$5 \mathrm{cm}, 4 \mathrm{cm}, 9 \mathrm{cm}$

$8 \mathrm{cm}, 7 \mathrm{cm}, 4 \mathrm{cm}$