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

What have to be the size of ZY to ensure that ZY to be tangent to circle X at level Y? 14 models 15 models 16 models 17 models

Step-by-step clarification: Within the picture connected you possibly can discover that line ZY is tangent at level Y. Do not forget that the radius is at all times perpendicular to tangents, by definition, which means . Which means is a proper triangle the place . All these info are deducted kind having ZY as a tangent. We all know by provided that , becaus it is the radius. Utilizing Pythagorean Theorem Fixing for Due to this fact, the size of ZY have to be 15 models to be tangent to circle X.

15 models Step-by-step clarification:

15 models Step-by-step clarification: The image of the query within the connected determine we all know that Triangle XYZ is a proper triangle, as a result of phase ZY is tangent to circle X at level Y so Making use of the Pythagorean Theorem we’ve substitute the given values

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reply: second choice step-by-step clarification: keep in mind the next theorem: “the tangent of a circle is perpendicular to the radius by means of the purpose of contact”. then, if the radius is perpendicular to the tangent, the angle shaped measures 90° levels. due to this fact, the triangle proven within the determine is a proper triangle. understanding this, you possibly can appply the pythagorean theorem to calculate the lenght zy: the place “a” is the hypotenuse and “b” and “c” are the legs of the fitting triangle. on this case: then it’s good to substitute values: and eventually you will need to remedy for zy:

c 16 Step-by-step clarification: edg

i consider it’s 15 Step-by-step clarification: Circle X is proven. Line phase X Y is a radius. Line phase Y Z is a tangent that intersects the circle at level Y. A line is drawn from level Z to level X and goes by means of a degree on the circle. The size of the road phase from level X to the purpose on the circle is 8, and the size of the road phase from the purpose on the circle to level Z is 9.
What have to be the size of ZY to ensure that ZY to be tangent to circle X at level Y?
14 models
15 models    needs to be 15 models 16 models      NOT 17 models

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The reply is 15 models!! Step-by-step clarification:

Hey! Keep in mind it’s a must to write full questions with the intention to get good and precise solutions. I will assume that you’ve got a circle X having two tangent traces that intersect at a degree outdoors the circle. From geometry, we all know that from any level outdoors a circle, two tangents to that circle are at all times congruent to one another in the event that they meet on the talked about level. So if the purpose of intersection known as Z, and a line is tangent to the circle at a degree Y, ZY have to be equal to ZW as a result of ZW is tangent to the identical circle at level W and meets ZY at a degree outdoors the circle, then it’s true that: So the ZY have to be equal 3 to ensure that ZY to be tangent to circle X at level Y

Unsure however i put 17 models

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