A circle is shown. Secant X Z and tangent W Z intersect at point Z outside of the circle. Secant X Z goes through the center of the circle and intersects the circle at point Y. The length of W Z is k + 4, the length of Z Y is k, and the length of X Y is 12. What is the length of line segment XZ?

Given:

Consider the below figure attached with this ques.

To find:

The length of the line segment XZ.

Solution:

According to the tangent-secant theorem, the square of tangent is equal to the product of secant and external segment of secant.

Using tangent-secant theorem, we get

Subtract both sides by 8k.

Divide both sides by 4.

Now,

Therefore, the measure of XZ is 16 units.

16.9 times 2.85

step-by-step explanation:

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