Discovering the Incenter of a Triangle: A Step-by-Step Guide to Find the Center of the Incircle

incenter

point of concurrency of angle bisectors, equidistant from triangle’s sides

Incenter is a point of concurrency in a triangle that lies inside the triangle and is equidistant from all three sides. In other words, it is the center of the circle which can be inscribed inside the triangle.

To find the incenter of a triangle, we need to follow the given steps:

1. Draw the given triangle.

2. Draw the perpendicular bisectors of any two sides of the triangle. The point where these two lines intersect is the center of the circle which can be inscribed inside the triangle.

3. Draw the third perpendicular bisector and extend it to meet the circle at point I. This point I is the incenter of the triangle.

Note that the incenter is equidistant from all three sides of the triangle, which means it lies on the angle bisectors of all three angles of the triangle. Also, the incenter is the center of the incircle which is the largest circle that can be inscribed inside the given triangle and touches all three sides of the triangle internally.

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