Power of a point

The term potency referred to a special geometry, by Jakob Steiner in 1826 introduced a measure of how far inside or outside of a circle is a point. The power of a point with respect to a circle having its center and radius is given by the arithmetic expression

Three cases can be distinguished:

• If the point is outside the circle, its potency is positive. If and the intersections of an arbitrary straight line through the circle, then the potency of after Sekantensatz same. This statement is also correct if and coincide ( secant tangent theorem). It follows from the Pythagorean theorem that the potency matches for a point P outside the circle with the square of the length of a tangent section ( in the drawing so with respectively).

• Points which lie on the circle having the 0 power

• For points in the circuit inside the power is negative. If and the intersections of an arbitrary straight line through the circle, then the power of the tendons after set equal.

Related terms

• Just potency