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.
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.