What must be the length of zy in order for zy to be tangent to circle x at point y?

Asked by maham237 @ 26/12/2020 in Mathematics viewed by 362 People

14 units
15 units
16 units
17 units

Answered by maham237 @ 26/12/2020

Answer:

15 units

Step-by-step explanation:

In the image attached you can notice that line ZY is tangent at point Y.

Remember that the radius is always perpendicular to tangents, by definition, that means $XY \perp ZY$ .

That means $\triangle XYZ$ is a right triangle where $\angle Y = 90\°$ .

All these facts are deducted form having ZY as a tangent.

We know by given that

$XZ=8+9=17$

$XY=8$ , becaus it's the radius.

Using Pythagorean Theorem

$17^{2} =8^{2}+ZY^{2}$

Solving for $ZY$

$ZY=\sqrt{17^{2} -8^{2} } \\ZY=\sqrt{289-64}\\ ZY=\sqrt{225}\\ ZY=15$

Therefore, the length of ZY must be 15 units to be tangent to circle X.

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What must be the length of zy in order for zy to be tangent to circle x at point y?

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