Question

Given: Circle k(O) Diameter

XY tangent WZ, XY = 10, and WZ = 12 .Find: YZ

Answer 1

Answer:

Side YZ is 8 units long.

Explanation:

Explanation:

We can deduct form the graph that segment WO is a radius of the circle and XY is its diameters.

By given, we know that , which means , by radius definition.

An important characteristic of tangents about circles is that the tangent is always is perpendicular to the radius, that means and is a right triangle, that means we can use Pythagorean's Theorem to find the side YZ.

Where is the hypothenuse and , are legs of the triangle.

Replacing all given values, we have

However, by sum of segments, we have

, where and

Therefore, side YZ is 8 units long.

Answer 2

Side YZ is 8 units long.

Explanation:

We can deduct form the graph that segment WO is a radius of the circle and XY is its diameters.

By given, we know that
`XY = 10`, which means
`WO=(XY)/(2)=(10)/(2)=5`, by radius definition.

An important characteristic of tangents about circles is that the tangent is always is perpendicular to the radius, that means
`\angle OWZ = 90\°\\` and
`\triangle OWZ` is a right triangle, that means we can use Pythagorean's Theorem to find the side YZ.

`OZ^(2) =WZ^(2)+OW^(2)`

Where
`OZ` is the hypothenuse and
`WZ` ,
`OW` are legs of the triangle.

Replacing all given values, we have

`OZ^(2)=12^(2)+5^(2)\\OZ=√(144+25)=√(169)\\ OZ=13`

However, by sum of segments, we have

`OZ=OY+YZ`, where
`OY=OW=5` and
`OZ=13`

`13=5+YZ\\YZ=13-5\\YZ=8`

Therefore, side YZ is 8 units long.