# Circle Properties: Area, Arc Length, Diameter, and Tangent

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## 16 Questions

A = πr²

Arc length

5 units

Central angle

120°

280°

120°

90°

### If the measure of an arc is 120°, which of the following statements is true?

The arc is a minor arc.

280°

40°

### If the measure of an intercepted arc is 270°, which of the following statements is true?

The intercepted arc is a semicircle.

240°

30°

## Study Notes

Circles are one of the most fundamental geometric shapes known to humanity, with their unique properties making them ubiquitous in mathematics, science, engineering, and art. In this article, we will explore some of these properties, including the circle's area, arc length, diameter, and tangent.

## Area

The area of a circle is calculated using its radius, which is half its diameter. The formula is given by:

A = πr²


where A represents the area and r is the radius of the circle. This means that if you know the radius of a circle, you can find its area simply by squaring the radius and multiplying it by π. For example, if a circle has a radius of 5 units, its area would be:

A = π(5²) = 25π


## Arc Length

The arc length of a circle is the distance between two points on the circle. It can be calculated using the formula:

L = 2rθ


where L represents the arc length, r is the radius of the circle, and θ is the central angle between the two points. This formula shows that the arc length of a circle is directly proportional to both the radius and the central angle.

## Diameter

The diameter of a circle is a measure of the circle's size, equal to the distance between two points on the circle that are farthest apart. The diameter is also the double of the radius. The formula for the diameter is:

D = 2r


where D represents the diameter and r is the radius of the circle.

## Tangent

A tangent is a line that touches a circle at a single point, referred to as a tangent point. The tangent is perpendicular to the radius of the circle at the point of contact. The tangent line can be found by extending a side of a right triangle that is inscribed in the circle, such that the hypotenuse is the diameter of the circle and the side is a chord of the circle.

In conclusion, circles have a rich array of properties and relationships that are crucial in various fields of study. Understanding these properties can help us better appreciate the beauty and elegance of this fundamental shape.

Explore the fundamental properties of circles such as area, arc length, diameter, and tangent. Learn how to calculate the area using the radius, determine the arc length based on the radius and central angle, understand the relationship between diameter and radius, and identify tangents to circles.

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