incenter of a Right | Acute | Obtuse Triangle

Definition:Triangle’s three angle bisectors(A bisector cuts an angle into two equal parts) intersect at a point and that point Known as incenter of a triangle.

Properties of incentre:
Draw a circle inside triangle(incircle), the largest circle that will fit inside the triangle and touch all three sides and centre of circle is known as an incenter of a triangle.

Triangle's incenter is always inside the triangle, it will never go outside the triangle
Incenter is equidistant(distance is equal) from all the sides of the triangle. 
The radius of the incircle is the length of the perpendicular line drawn from the Incenter to any side 

Figure 1: incenter and incircle of a triangle
Incentre and Incircle of Acute Triangle:
Acute Triangle’s three angle bisectors(A bisector cuts an angle into two equal parts) intersect at a point and that point is incenter of an Acute triangle.The largest circle that will fit inside the Acute triangle and touch all three sides Known as Incircle of Acute Triangle.
Figure 2: incenter and incircle of an acute triangle

Incentre and Incircle of Obtuse Triangle:
Obtuse Triangle’s three angle bisectors(A bisector cuts an angle into two equal parts) intersect at a point and that point is incenter of an Obtuse triangle.The largest circle that will fit inside the Obtuse triangle and touch all three sides Known as Incircle of Obtuse Triangle.
Figure 3: incenter and incircle of an obtuse triangle

Incentre and Incircle of Right Triangle:
Right Triangle’s three angle bisectors(A bisector cuts an angle into two equal parts) intersect at a point and that point is incenter of a Right triangle.The largest circle that will fit inside the Right triangle and touch all three sides Known as Incircle of Right Triangle.
Figure 4: incenter and incircle of a right triangle
Description
The incenter is the point of intersection of the three angle bisectors. The angle bisectors of a triangle are each one of the lines that divide an angle into two equal angles. The incenter is the center of the circle inscribed in the triangle.

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