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What is the length XPY in terms of pi? A. 24pi B. 12pi C. 4pi D. 720pi

What is the length XPY in terms of pi? A. 24pi B. 12pi C. 4pi D. 720pi

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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What is the length XPY in terms of pi?

A. 24pi

B. 12pi

C. 4pi

D. 720pi

**Circle Diagram Explanation** This diagram features a circle with some labeled elements: 1. **Circle Overview**: - The full circle is depicted. - Points X, Y, and P are marked on the circumference of the circle. 2. **Radius**: - A radius of the circle is drawn from the center to a point on the circumference (Y). - The length of the radius is labeled as 8 meters. 3. **Right Angle Indicator**: - Point X is directly above the center, forming a vertical line. - Point Y forms a horizontal line extending to point on the circumference. - These lines intersect at a right angle (90 degrees). 4. **Point P**: - Point P is another point marked on the circumference of the circle, away from X and Y. **Detailed Diagram Analysis**: - **Right Triangle**: - The diagram contains a right triangle formed by points X, Y, and the center of the circle. - The right angle is at the intersection of the lines connecting X and Y to the circle's center. - One leg of the triangle runs vertically from the center up to point X. - The other leg extends horizontally from center to point Y. - The hypotenuse of the triangle is the radius of the circle, connecting point Y with the center. - **Radius Information**: - Given the radius (distance from the center to any point on the circumference) is 8 meters, we can infer various properties of the circle and right triangle. - Sometimes, such diagrams are used to compute areas, perimeters, or understanding trigonometric properties. This diagram is useful in understanding basic geometric properties of circles and right triangles, often applicable in geometry and trigonometry problems.
Transcribed Image Text:**Circle Diagram Explanation** This diagram features a circle with some labeled elements: 1. **Circle Overview**: - The full circle is depicted. - Points X, Y, and P are marked on the circumference of the circle. 2. **Radius**: - A radius of the circle is drawn from the center to a point on the circumference (Y). - The length of the radius is labeled as 8 meters. 3. **Right Angle Indicator**: - Point X is directly above the center, forming a vertical line. - Point Y forms a horizontal line extending to point on the circumference. - These lines intersect at a right angle (90 degrees). 4. **Point P**: - Point P is another point marked on the circumference of the circle, away from X and Y. **Detailed Diagram Analysis**: - **Right Triangle**: - The diagram contains a right triangle formed by points X, Y, and the center of the circle. - The right angle is at the intersection of the lines connecting X and Y to the circle's center. - One leg of the triangle runs vertically from the center up to point X. - The other leg extends horizontally from center to point Y. - The hypotenuse of the triangle is the radius of the circle, connecting point Y with the center. - **Radius Information**: - Given the radius (distance from the center to any point on the circumference) is 8 meters, we can infer various properties of the circle and right triangle. - Sometimes, such diagrams are used to compute areas, perimeters, or understanding trigonometric properties. This diagram is useful in understanding basic geometric properties of circles and right triangles, often applicable in geometry and trigonometry problems.
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