In the circle, AB=42,BC=18, and CD=4. The diagram is not drawn to scale.

the picture in the attached figure

we know that
The Intersecting Secants Theorem, states 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
in this problem
(x+DC)*DC=(AB+BC)*BC
AB=42
BC=18
CD=4
(x+4)*4=(42+18)*18
4x+16=1080
4x=1080-16
x=1064/4
x=266

the answer is
x=266

Answer Link

abidemiokin abidemiokin · Answer 2 · 2022-03-24T11:49:46+01:00

The value of x from the given diagram is 266

Intersecting chord theorem;

According to the theorem; ''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''

From the figure shown, we will have the expression

(x+DC)*DC=(AB+BC)*BC

Given the following parameters;

AB=42

BC=18

CD=4

Substitute to have:

(x+4)*4=(42+18)*18

4x+16=1080

4x=1080-16

x=1064/4

x=266

Hence the value of x from the given diagram is 266

Learn more on secant theorem here: https://brainly.com/question/10732273