Power-of-a-point theorem

Take a line through a given point P cutting a circle with centre M and radius r. The product of the distance of the point to one intersection point and the distance to the other intersection point is constant, which is called the power of the point. This power is also equal to |PM|2-r2.

If the point lies inside the circle, this theorem is equivalent to the Intersecting chords theorem. It is also the basis for the Tangent-secant theorem.

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