Consider circle O. If AE = 7, EC = 2, and BE = 4, what is ED?

1 Answer

• We know that ∆AEB is similar to ∆DEC.

  Thus, AE and BE are proportional to DE and CE, respectively.

  Since we know that the triangles are similar and that BE = 4 and CE = 2, we can infer that each side ∆AEB is twice as large as its counterpart in ∆DEC.

  We know that AE = 7; therefore, its corresponding side, ED, must be half that length.

  Therefore, ED = 3.5