Concurrent lines all intersect at the same point, and all meet at a central location in a shape. How these are found, and calculated differ based on the individual shape. Let us explore how some shapes utilize concurrent lines.
Medians-Centroid:
A line drawn from any vertex to the mid point of its opposite side is called a median with respect to that vertex. Thus, a triangle has 3 medians and all the 3 medians meet at one point. i.e. the medians of a triangle are concurrent.
The point of concurrency of medians is called centroid of the triangle.
Altitudes of a triangle:
A perpendicular line segment drawn from a vertex to its opposite side is called the altitude of the triangle with respect to that vertex. Thus, a triangle has 3 altitudes and all the 3 altitudes meet at one point. . i.e. the altitudes of a triangle are concurrent.
The point of concurrency of altitudes is called orthocenter of the triangle.
Angular Bisectors – Incenter:
The bisectors of the angles in atriangle meet at one point. i.e. the angular bisectors of a triangle are concurrent.
The point of concurrency of angular bisectors is called incenter of the triangle. If we draw a circle taking the incenter as the centre and the distance from the incenter to any side of the triangle as the radius then we get a circle which touches all the sides of the triangle which is known as the incircle.
Perpendicular Bisectors – Circumcenter:
A perpendicular bisector of a side of a triangle is a line which is perpendicular to the side and drawn at the mid point of the same side. There will be 3 perpendicular bisectors in a triang;e and all of them meet at one points. i.e. the perpendicular bisectors of a triangle are concurrent.
The point of concurrency of perpendicular bisectors is called circumcenter of the triangle. If we draw a circle taking the circumcenter as the centre and the distance from the circumcenter to any vertex of the triangle as the radius then we get a circle which touches all the vertices of the triangle which is known as the circumcircle.
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