Three circles intersect at one point

Sometimes, when you draw three different circles in a plane, they can all pass through a single common point. A classic example is when you have a triangle, and you draw the circumcircles of three triangles formed by picking three points on the triangle's sides (such as the Miquel point configuration). The point where all three circles meet is called the point of concurrency.

Important properties

• If three circles each pass through two vertices of a triangle and a point on the opposite side, they can all intersect at a single point.

• This point of intersection is unique for the given configuration.

• The concurrency often arises from properties of inscribed angles and cyclic quadrilaterals.