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{{ printedBook.courseTrack.name }} {{ printedBook.name }} If two secants intersect in the exterior of a circle, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.

Base on the diagram above, the following relation holds true.

$EA⋅EB=EC⋅ED$

This theorem is also known as the **Secant Segments Theorem** or the **Intersecting Secants Theorem**.

Consider the auxiliary segments $AD$ and $BC.$

Notice that $∠EBC≅∠EDA$ because these two inscribed angles intercept the same arc, $AC.$

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In consequence, $△EDA∼△EBC$ thanks to the Angle-Angle Similarity Theorem. This allows to set the following proportion. $ECEA =EBED $ Finally, by cross multiplying, the desired result is obtained.

$EA⋅EB=EC⋅ED$