Find the value of EC

thank you in advance for the help!

EC = 8

Step-by-step explanation:

Firstly note that the radius of the circle is 13 ( centre to D )

Thus the distance from B to the centre is 13

Thus B → E → centre is a right triangle and distance from centre to E (x) can be calculated using Pythagoras' identity, that is

x² + 12² = 13²

x² + 144 = 169 ( subtract 144 from both sides )

x² = 25 ( take the square root of both sides )

x = = 5

The distance from the centre to C ( the radius ) is 13, thus

x + EC = 13, that is

5 + EC = 13 ( subtract 5 from both sides )

EC = 8