   Chapter 6.1, Problem 43E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In ⊙ O , O Y = 5 and X Z = 6. If X W ¯ ≅ W Y ¯ , find W Z . To determine

To calculate:

The WZ by using the provided figure.

Explanation

Given: In O, OY=5, and XZ=6 if XW¯WY¯

Pythagorean Theorem:

In a right triangle XYZ, (XY)2+(YZ)2=(XZ)2.

Calculation:

We need to find WZ.

Let WZ=y and x represent the measure of the congruent segments XW¯WY¯.

Since, OY=5 is a radius of circle O.

We know that, the diameter is double the radius of the circle.

Thus, XY=10.

Since, XYZ and XWZ are right triangles.

Thus, by using the Pythagorean theorem for XYZ triangle.

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