Secant Secant Theorem

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Let $C$ be a point external to a circle $ABED$.

Let $CA$ and $CB$ be straight lines which cut the circle at $D$ and $E$ respectively.


$CA \cdot CD = CB \cdot CE$



Draw $CF$ tangent to the circle.

From the Tangent Secant Theorem we have that:

$CF^2 = CA \cdot CD$
$CF^2 = CB \cdot CE$

from which the result is obvious and immediate.


Also known as

This result is also known as the intersecting secant theorem or just the secant theorem.

Also see

This result is a generalization of the Intersecting Chord Theorem where the point of intersection of the two lines is outside the circle.

The Power of a Point Theorem is a generalization of both.