Question

In the circle AB=19, BC=10, and CD=5. The diagram is not drawn to scale.

Answer 1

We know that
If two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.

so
BC*AC=CD*(x+CD)
AB=19
BC=10
CD=5
AC=AB+BC----> AC=29
(x+CD)=BC*AC/CD-----> 10*29/5-----> 58
(x+CD)=58------> x=58-CD-----> x=58-5----> x=53

Answer 2

To solve the problem above, you must apply the proccedure shown below:

 1. You have that in the circle AB=19, BC=10, and CD=5.

 2. Then, to calculate the value of "x", you must apply the Intersecting secant theorem, as below:

 (BC)(AC)=(CD)(xC)

 BC=10

 AC=AB+BC
 AC=19+10
 AC=29

 CD=29

 xC=x+CD=(5+x)

 3. Now, you must susbtitute the values shown above into the formula and then, you must clear "x", as below:

 (10)(29)=(5)(x+5)
 290=5x+25
 290-25=5x
 265=5x
 x=265/5

 4. Then, you have that the value of "x" is:

 x=53

 5. Therefore, as you can see, the answer is:

 x=53