Question

In the accompanying diagram of circle O, chords AB and CD intersect at E. If AE = 4, EB = 9, and CE = 6, what is the length of ED?

Answer 1

`ED=6\ units`

Explanation:

we know that

The intersecting chords theorem is a statement that describes a relation of the four line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal

so

In this problem

`(AE)(EB)=(CE)(ED)`

substitute the given values

`(4)(9)=(6)(ED)`

solve for ED

`ED=36/6\\ED=6\ units`