A Mathematical Blog

Centroid of Triangle Previously, i have written about the Circumcenter and the Incenter, which are two of the four centers of a triangle covered in this blog. The other two centers are the Centroid and the Orthocenter. These four centers are the points in the plane of a triangle with some interesting properties. Circumcenter is the point  equidistant from the three vertices of a triangle. It is also the point where the three perpendicular bisectors of the three sides of the triangle meet. Circumcenter may lie inside or outside of the triangle depending on what type of triangle it is. To know more about the circumcenter, click here . Incenter is the point which is  equidistant from the three edges . It is also the point of concurrency of the three angle bisectors of the three interior angles of triangle . Unlike Circumcenter, Incenter is always present inside of any triangle. To know more about the incenter, click here . Now let’s talk about the Cen...

In this post, we will talk about the Incenter, another one of those centers of a triangle. It also has the word ‘center’ in it.  Incenter, often denoted by letter I , is the center of the INCIRCLE of a triangle.  Incircle is the name given to a circle of maximum possible radius that completely sits inside of the triangle. Out of all possible circles contained in a triangle, the biggest of all is the incircle, marked with a green outline in the picture below.  One property of an Incircle is that it “touches” the three edges of a triangle. Or the three edges are three tangents to the incircle, as shown in the picture above.  In general, tangent at any point of a circle is perpendicular to the radius at that point. So the three edges of a triangle must be perpendicular to the three radii of the incircle at points of tangencies, as depicted in the image below.  Because of this, the incenter is also said to be the point which is same ‘perpendicular dis...