Circle X is shown. Line segment X Y is a radius. Line segment Y Z is a tangent that intersects the circle at point Y. A line is drawn from point Z to point X and goes through a point on the circle. The length of the line segment from point X to the point on the circle is 8, and the length of the line segment from the point on the circle to point Z is 9.
What must be the length of ZY in order for ZY to be tangent to circle X at point Y?

14 units
15 units
16 units
17 units

Circle X is shown. Line segment X Y is a radius. Line segment Y Z is a tangent that intersects the circle at point Y. A line is drawn from point Z to point X and goes through a point on the circle. The length of the line segment from point X to the point on the circle is 8, and the length of the line segment from the point on the circle to point Z is 9.

What must be the length of ZY in order for ZY to be tangent to circle X at point Y?

14 units

15 units should be 15 units

16 units NOT

17 units

Lanuel Lanuel · Answer 2 · 2022-07-05T13:40:19+02:00

By applying Pythagorean' theorem, the length of ZY to be tangent to circle X is equal to: B. 15 units.

How to determine the length of ZY?

Since line ZY is tangent at point Y and the radius of a circle is always perpendicular to tangents, we can deduce the following points:

Line segment XY is perpendicular line segment ZY.

Triangle XYZ is a right-angled triangle.

Thus, the length of XZ is given by:

XZ = 8 + 9

XZ = 17 units.

Next, we would apply Pythagorean' theorem to find the required length of ZY:

XZ² = ZY² + XX²

17² = ZY² + 8²

ZY² = 289 - 64

ZY = √225

ZY = 15 units.

Read more on Pythagorean theorem here: brainly.com/question/23200848

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