Answer:
[tex]\Delta \text{RPT is an isosceles triangle}[/tex]
Step-by-step explanation:
As in the triangle RST,
[tex]RS=ST\ \ \ \Rightarrow m\angle SRT=m\angle STR[/tex]
Because if in a triangle two angles equal one another, then the sides opposite the equal angles also equal one another.
Incenter is obtained by the Intersection of a triangle's three angle bisectors and it is equidistant from the three sides of the triangle.
So, RP and TP are the angle bisectors of ∠R and ∠T respectively.
[tex]\Rightarrow \dfrac{m\angle SRT}{2}=\dfrac{m\angle STR}{2}[/tex]
[tex]\Rightarrow m\angle PRT=m\angle PTR[/tex]
[tex]\Rightarrow PR=PT[/tex]
[tex]\Rightarrow \Delta \text{RPT is an isosceles triangle}[/tex]
