In $\Delta ABC$,if $\angle A = \angle B = \angle C$,then $\angle B = \dots$ (in $^{\circ}$)

In $\Delta PQR$,$S$ is any point in its interior. Prove that $SQ + SR < PQ + PR$.

In a huge park,people are concentrated at three points (see Fig) :
$A$ : where there are different slides and swings for children,
$B$ : near which a man-made lake is situated,
$C$ : which is near to a large parking and exit. Where should an ice cream parlour be set up so that the maximum number of persons can approach it?
(Hint: The parlour should be equidistant from $A$,$B$,and $C$.)

$ABC$ is a triangle. Locate a point in the interior of $\Delta ABC$ which is equidistant from all the vertices of $\Delta ABC$.

If one angle of a triangle is equal to the sum of the other two angles,then the triangle is

In the figure,$AD$ is the bisector of $\angle BAC$. Prove that $AB > BD$.