Let C be a circle and let 𝒟 be the set of all diameters of C. What is ∩𝒟 ? (Here, by "diameter"

Name: Problem 104, Chapter 1: Discrete Mathematics
Uploaded: 2022-10-09T05:53:13-08:00
Duration: 1 min 32 s
Channel: Manisha Sarker
Description: Let C be a circle and let 𝒟 be the set of all diameters of C. What is ∩𝒟 ? (Here, by "diameter" we mean a line segment through the center of the circle with its endpoints on the circumference of the circle.)

step 1 In this problem, it is said that C is a circle, and this set D is the set of all diameters of C.

Question

Let $C$ be a circle and let $\mathcal{D}$ be the set of all diameters of $C$. What is $\cap \mathcal{D} ?$ (Here, by "diameter" we mean a line segment through the center of the circle with its endpoints on the circumference of the circle.)

   Let $C$ be a circle and let $\mathcal{D}$ be the set of all diameters of $C$. What
is $\cap \mathcal{D} ?$ (Here, by "diameter" we mean a line segment through the center of the circle with its endpoints on the circumference of the circle.)

Discrete Mathematics

Richard Johnsonbaugh 8th Edition

Chapter 1, Problem 104

Instant Answer

Solved by Expert Manisha Sarker

10/09/2022

Step 1

A diameter is a line segment that passes through the center of the circle and has its endpoints on the circumference of the circle. Show more…

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Let $C$ be a circle and let $\mathcal{D}$ be the set of all diameters of $C$. What is $\cap \mathcal{D} ?$ (Here, by "diameter" we mean a line segment through the center of the circle with its endpoints on the circumference of the circle.)

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Key Concepts

Set Intersection

The intersection of a collection of sets is the set of all elements that are common to every set in the collection. In geometric contexts, finding the intersection of all diameters involves identifying the point or points that lie on every one of these line segments, highlighting the pervasive role of the center in the circle.

Circle

A circle is the set of all points in a plane that are equidistant from a fixed point, known as the center. This concept is fundamental in geometry and provides the basis for understanding various properties such as circumference, area, and the behavior of chords and diameters.

Diameter

A diameter is a specific type of chord in a circle that passes through the center, connecting two points on the circumference. It is the longest possible chord in a circle, and its properties are essential for understanding symmetry and centrality in circular geometry.

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