A circle is a shape we all are familiar with, but many of us don’t know the properties of circles. They can be observed everywhere around us. It is a shape that is of great importance. The tyres of a vehicle are all in the shape of a circle, as they can be rolled easily. Similarly, circles are used in many places. In this article, we will go through a few of the properties of circles and understand their importance. This will also help students to understand this shape better and solve problems related to them easily.
A circle is a two-dimensional shape. A circle is one of those shapes that does not contain even a single edge or a corner. It is completely round with zero edges and corners. There are various crucial concepts related to circles, but radius and diameter are the basic concepts to study before moving to other properties.
Whenever we have to construct a circle, there is one necessary condition that should be known to us, and that is the radius or diameter of the circle. The diameter of the circle always crosses the midpoint of the circle and is the longest chord inside a circle. Endpoints of a diameter always lie exactly opposite to each other. One more point about the endpoints of the diameter is that they always lie on the circle. One can simply say that half the diameter is called a radius. The radius of a circle is always equal to half the value of the diameter. For instance, let us take the diameter of a circle to be of length z, then the radius is given by z/2. Similarly, if the radius is given to us, let us say y. Then we can calculate the diameter of the circle by multiplying it by a factor of 2. Thus, the diameter will be 2*z. Now, let us look at two of the most critical properties of a circle and they are the area and circumference of a circle.
The circumference can be defined as the length of the boundary of the circle. It is crucial to know about the formula to calculate it easily. To calculate the circumference of a circle we need to know the radius of the circle or the diameter of the given circle. The circumference is always given by the formula 2πr, where r is the radius of the given circle. Another way of representing the same formula is πd, where d is the diameter of the circle whose circumference is to be found. To get the area of a circle we always use the formula πr2. In this formula, r is the radius of the circle whose area is to be found and π is a universal constant.
The word tangent means to touch. In geometry, a tangent refers to a line or a plane that touches or intersects a curve at one point only. If there is a line or a plane that touches a line more than one point, then it can never be a tangent. One more type of tangent is there, that we study in trigonometry. Here we are discussing tangents related to geometry. There are different equations of representing a tangent depending on the curves to which a tangent is drawn. Most of the time, to write an equation for the tangent. We are required to have the slope of the tangent. The slope of the tangent can be found by differentiating the function at the given point of contact.
The above concept of tangents and circles are crucial for students to master, as they are used for our whole life and are the basic concepts. Nowadays, there are online platforms that are helping students to master these topics. Cuemath is one of those excellent platforms that nurtures the students for the future.