As the title suggests, I would like to ask if I have two equations of circle that coincide, are they considered tangent to one another?
I am currently working on a proof of Feuerbach's Theorem (1822) which states that the nine-point circle of a triangle is tangent to the incircle and the point of tangency of these two circles is called the Feuerbach point of the triangle.
I have stumbled upon a case where the triangle is equilateral and
the incircle and the nine-point circle coincide. In this case, can we consider these circles as tangent to one another?
Best Answer
No, two circles are tangent only if they meet at exactly one point.