Given: AB = 6, AD = x, CD = 16, and CB = 12.

What is the value of x?

Given:

AB = 6, AD = x, CD = 16, and CB = 12.

To find:

The value of x.

Solution:

Consider the below figure attached with this question.

In the figure BD is the angle bisector. So, using angle bisector theorem, BD divides the opposite sides in the ratio of other two sides.

Multiply both sides by 16.

Therefore, the value of x is 8.

x = 17

step-by-step explanation:

in the given figure, two triangles are inscribed in a circle where ∠bae ≅ ∠dae which makes the side be and de equal so we can write it as:

3x - 24 = x + 10

solving this equation for x to get:

3x - x = 10 + 24

2x = 34

x = 34/2

x = 17

therefore, the value of x = 17.