The power of a point A (circle power,power of a circle) with respect to a circle with center 0 and radius r is defined as Image File history File links Circlepower. ... In Euclidean geometry, a circle is the set of all points at a fixed distance, called the radius, from a fixed point, called the centre (center). ...

(AO)² − r².

Therefore points inside the circle have negative power, points outside have positive power, and points on the circle have power zero.

The theorem of intersecting chords (or chord-chord power theorem) states that if P is a point inside a circle and AB and CD are chords of the circle intersecting at P, then A chord of a curve is a geometric line segment whose endpoints both lie on the curve. ...

The common value of these products is the negative of the power of the point P with respect to the circle (since the power is negative and the product of positive lengths is positive).

The theorem of intersecting secants (or secant-secant power theorem) states that if AB and CD are chords of a circle which intersect at a point P outside the circle, then

In this case the common value is the same as the power of P because both are positive.

When expressed in this form it becomes clear that both theorems are really special cases of the more general power of a point theorem, which covers both these cases as well as the limiting cases where two points coincide and their secant becomes a tangent. In mathematics, the word tangent has two distinct, but etymologically related meanings: one in geometry, and one in trigonometry. ...

External links

• Power of a Point Theorem at cut-the-knot
• Eric W. Weisstein. "Circle Power." From MathWorld--A Wolfram Web Resource
• Intersecting Chords Theorem at cut-the-knot