We will discuss here the Incircle of a triangle and the incentre of the triangle.
The circle that lies inside a triangle and touches all the three sides of the triangle is known as the incircle of the triangle.
If all the three sides of a triangle touch a circle then the sides of the triangle are tangents to the circle. Hence, the centre of the circle is located at the point of intersection of the internal bisectors of the angles of the triangle. This point is called the incentre of the triangle and is equidistant from the sides of the triangle.
The radius of this circle is equal to the shortest (perpendicular) distance between the incentre and any one of the sides.
Here, the incircle of ∆XYZ is the circle with centre O and radius equal to OA, or OB, or OC.
Also, XB = XC, YA = YB and ZA = ZC.