Question

A circle is shown. Chords A C and B D intersect at point E.
Chords AC and BD intersect at E, with BD = 7 units, DE = 2 units, and AE = 4 units.



What is the length of segment CE?

units

Answer 1

By the intersecting chords theorem, AE·CE = BE·DE. Here BE = BD − DE = 7 − 2 = 5, so
4·CE = 5·2 = 10, hence CE = 10/4 = 2.5 units.