8. Can someone explain how to solve this?

Question

asked Apr 10, 2021 102k views

1 Answer

EddieDean · Answer 1 · 2021-04-15T22:37:25+0000

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:

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