26. Circles and their properties

The circle is one of the most fundamental geometric shapes in mathematics and has several properties that are important for understanding many mathematical concepts. In the context of ENEM preparation, it is crucial to understand the properties of circles and how they apply to practical problems.

First, let's define what a circle is. A circle is the set of all points in a plane that are at a certain distance, known as the radius, from a fixed point, called the center. The line connecting all these points is called the circumference of the circle.

One of the most basic properties of a circle is that all lines drawn from the center of the circle to the circumference (the edge of the circle) are equal in length. This is what defines the radius of a circle. Furthermore, the diameter of a circle, which is a line passing through the center of the circle and touching the circumference on both sides, is always twice the length of the radius.

The circumference of a circle is given by the formula C=2πr, where C is the circumference, r is the radius, and π is a constant whose approximate value is 3.14159. The area of ​​a circle is given by the formula A=πr², where A is the area and r is the radius.

Another important property of circles is that any angle inscribed in a circle that intersects the same arc on the circumference is equal. This is known as the inscribed angle property. Furthermore, the angle formed by two lines tangent to a circle from an external point is always equal to 90 degrees.

Circles also have several properties related to the lines and segments that intersect them. For example, a chord is a line connecting two points on the circumference of a circle. Diameter is the largest possible chord in a circle. A secant segment is a line that intersects a circle at two points, while a tangent is a line that touches a circle at exactly one point.

There are also several properties related to circles and triangles. For example, the inscribed angle theorem states that the angle formed by two points on the circumference of a circle is always half the corresponding central angle. Furthermore, the chord theorem states that if two chords of a circle are equal in length, then they intersect equal arcs on the circumference.

In summary, circles are fundamental geometric shapes with a wealth of properties that are crucial to understanding mathematics. When preparing for the ENEM, it is important to understand these properties and how they apply to a variety of mathematical problems.

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