Question

8. Can someone explain how to solve this?

Answer 1

Answer:
`EC=1.928`

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:

`EC*BE=AE*DE`

You can identify that:

`BE=14\\\\AE=3\\\\DE=AD-AE=12-3=9`

Now you have to susbstitute those lengths into the equation:

`EC*14=3*9`

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

`EC*14=27\\\\EC=(27)/(14)\\\\EC=1.928`