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If two chords intersect in the interior of a circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.
Based on the diagram above, the relation below holds true.
AE* EB = CE * ED
This theorem is also known as the Intersecting Chords Theorem.
Because ∠ CAB and ∠ CDB are inscribed angles that intercept the same arc CB, they are congruent angles. Similarly, ∠ ACD and ∠ ABD are inscribed angles that intercept the same arc AD. Therefore, they are also congruent angles.
Consequently, by the Angle-Angle Similarity Theorem, △ AEC and △ DEB are similar triangles. This relationship means that the following proportion can be set. AE/ED = CE/EB Finally, by cross multiplying, the desired result is obtained.
AE* EB = CE * ED