Sign In
Based on the diagram above, the relation below holds true.
AE* EB = CE * ED
This theorem is also known as the Intersecting Chords Theorem.
Consider the auxiliary segments AC and BD.
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