Circle Terminology and Properties

Questions and Answers

What is the definition of a circle?

An arc of a circle having a measure less than 180 degrees

The distance from the center of a circle to any point on the circle

The set of all points in a plane that are the same distance from a given point called the center (correct)

A line that intersects a circle in two points

What is the center point of a circle?

Point found in the center of a circle

What is the diameter of a circle?

Half of a circle

The distance from the center to any point on the circle

A chord that passes through the center of the circle (correct)

The perimeter of a circle

Define the radius of a circle.

The distance from the center of a circle to any point on the circle Signup and view all the answers

What is the circumference of a circle?

The perimeter of a circle or distance around the circle Signup and view all the answers

What is a chord?

A segment whose endpoints are on a circle Signup and view all the answers

What does Pi represent?

The ratio of the circumference of a circle to its diameter Signup and view all the answers

What does the Tangent to a Circle Theorem state?

A line drawn tangent to a circle is perpendicular to a radius of the circle drawn to the point of tangency Signup and view all the answers

What is a secant of a circle?

A line that intersects a circle in two points Signup and view all the answers

Define a semi-circle.

Half of a circle Signup and view all the answers

What is a central angle of a circle?

An angle whose vertex is the center of the circle Signup and view all the answers

What is the intercepted arc in circles?

Angle is 1/2 of the intercepted arc Signup and view all the answers

What is a major arc?

An arc of a circle whose measure is greater than 180 degrees Signup and view all the answers

What is a minor arc of a circle?

An arc of a circle having a measure less than 180 degrees Signup and view all the answers

Define the sector of a circle.

A region bounded by an arc of the circle and the two radii to the arc's endpoints Signup and view all the answers

The formula to find the length of arc is: Central Angle/360 = ______/Circumference

Arc Length Signup and view all the answers

What is the area of a circle?

Total space contained in the circle Signup and view all the answers

What is another definition for sector of a circle?

The region bounded by two radii of the circle and their intercepted arc Signup and view all the answers

What is the equation of a circle in standard form?

(x-h)² + (y-k)² = r² Signup and view all the answers

Study Notes

Circle Terminology and Properties

A circle is defined as the collection of all points in a plane equidistant from a central point, known as the center.
The center point serves as the focal point for the circular shape.
The diameter of a circle is a special type of chord that passes directly through the center, dividing the circle into two equal halves.
A radius is the distance from the center to any point along the circle's edge, with all radii being equal in length.
Circumference refers to the total distance around the circle, equivalent to the perimeter of a circular shape.
A chord is defined as a line segment whose endpoints lie on the circumference of the circle.

Mathematical Constants and Theorems

Pi (π) is approximately 3.14159 and represents the ratio of the circumference of a circle to its diameter, fundamental in circle calculations.
According to the Tangent to a Circle Theorem, a line that is tangent to the circle forms a right angle with the radius at the point of tangency.
A secant intersects a circle at two distinct points, indicating the line extends through the circle's area.

Arc and Angle Definitions

A semi-circle is simply half of a full circle, measured as 180 degrees.
The central angle of a circle is formed by two radii, with the vertex located at the circle's center.
The intercepted arc connected to a central angle is significant, as the measure of the angle is half that of the arc.
A major arc spans an angle greater than 180 degrees, while a minor arc measures less than 180 degrees.

Areas and Sections of Circles

A sector of a circle is the area enclosed by two radii and their corresponding arc, resembling a slice of pizza.
The length of an arc can be calculated using the relationship: Central Angle/360 = Arc Length/Circumference.
The area of a circle quantifies the total space enclosed within its boundary, necessary for various applications in geometry.

Circle Equations

The standard form equation for a circle is represented as (x-h)² + (y-k)² = r², where (h, k) indicates the center coordinates, and r signifies the radius.

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Description

This quiz explores the fundamental terminology and properties of circles, including definitions of key terms like center, diameter, radius, and circumference. It also covers essential mathematical constants such as pi (π) and associated theorems. Test your understanding of circular geometry!