contestada

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?

Respuesta :

calculista

Answer:

[tex]ED=6\ units[/tex]

Step-by-step 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

[tex](AE)(EB)=(CE)(ED)[/tex]

substitute the given values

[tex](4)(9)=(6)(ED)[/tex]

solve for ED

[tex]ED=36/6\\ED=6\ units[/tex]

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