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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.
AE⋅EB=CE⋅ED