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Intersecting Secants Theorem

High School Math based on the topics required for the Regents Exam conducted by NYSED.

Intersecting Secant Theorem

If two secant segments are drawn to a circle from the same external point, the product of the length of one secant segment and its external part is equal to the product of the length of the other secant segment and its external part.

For example, in the following diagram PA × PD = PC × PB

Power of a point with two secant segments

Secants :
A secant is a line, ray, or line segment that intersects a circle in two places.
Three points are covered:
(1) secants that intersect in a circle which divide each other proportionally,
(2) the angle formed by secants which intersects in a circle and is half the sum of the intercepted arcs, and
(3) two secants drawn from the same point outside a circle that form an angle whose measure is half the difference of the intercepted arcs.

Intersecting secant theorem

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