Respuesta :

Answer: [tex]EC=1.928[/tex]

Step-by-step explanation:

For this exercise you need to remember the Intersecting Chord Theorem.

The Intersecting Chord Theorem states that if two chords are intersecting inside a circle, the products of their segments are equal.

Therefore, based on this and observing the given figure, you know that:

[tex]EC*BE=AE*DE[/tex]

You can identify that:

[tex]BE=14\\\\AE=3\\\\DE=AD-AE=12-3=9[/tex]

Now you have to susbstitute those lengths into the equation:

[tex]EC*14=3*9[/tex]

Finally, you must solve for EC in order to find its length. You get that this is:

[tex]EC*14=27\\\\EC=\frac{27}{14}\\\\EC=1.928[/tex]