Point of concurrency is the Intersection Point of three or more lines. These lines must be concurrent. Angle bisectors (in center), medians (centroid), normal bisectors (ortho center) and altitudes (circumcenter) are concurrent in every triangle. Parameters within the blocks are of four types for explanation of Triangles.
Figure shows a Graphical representation of point of concurrency.
In the above figure, three lines are intersecting at same point 'p'. Hence point 'p' is called as point of concurrency. Lines which are intersecting must be concurrent.
Let’s consider three lines shown below to understand how to find the point of concurrency.
p 1 x + q 1 y + r 1 = 0, p 2 x + q 2 y + r 2 = 0 and p 3 x + q 3 y + r 3 = 0. Conditions of concurrency must be fulfilled for these lines to be concurrent. These conditions are as follows:
│ p1 q1 r1 |
| p2 q2 r2 |
| p3 q3 r3 │ must be equals to zero.
2) There exists three constants j, k, l (≠ zero at the same time) such that j I 1 + k I 2 + l I 3 = 0, where I1 = 0, I2 = 0 and I3 = 0 are three given straight lines.
3) Three lines are concurrent if any one of the lines passes through the point of intersection of other two lines or if two or more lines pass through a single point.
There is a major difference between point of concurrency and the point of intersection. Point of concurrency is the intersection point of concurrent lines such as perpendicular bisectors of sides of a triangle are concurrent and they meet at point of concurrency. Point of intersection may be the point where two or more lines meet.