Question

if EB=7, find the value of CD

Answer 1

Both lines AB and CD are secant lines beacuse in two points they are touching the circunference. There is a Theorem which says the following

$PB\cdot PA=PD\cdot PC$

Since the distance from the center of the circle to each secant line is the same (5 units), we could assume that the both secant lines are similar. saying:

$PB=PD;\text{ }PA=PC\Rightarrow AB=CD$

Then the lenght of CD is:

$CD=2\cdot EB=2(7)=14$