![]() What is the diameter of a circle whose radius is 3 times that of the given circle? Find the diameter of a circle whose radius is 10 cm. cm.Įxample 2: Tell whether the given statement is true or not: If the endpoints of the diameter of the circle are given, then to find the coordinates of the center we use the mid-point formula.Īns: True, if the endpoints of the circle's diameter are given, then to find the coordinates of the center we use the mid-point formula. Therefore, the area of the circular region is 1848 sq. ![]() In the case of L, it is 4 cm away from I and 2cm away from J while in the case of K, it is 3cm away from I and 3cm away from J so we will conclude K is the midpoint or center of the line segment.Īll mathematical drawings and images were created with GeoGebra.The Lines Intersecting is the Center of the CircleĮxample 1: Find the area of a circle whose radius is 28 cm. D ividing this distance by 2 gives us 3cm, so we will now look at the point that is 3cm away from I and J. To find the center, we will first find the distance between I and J which turns out to be 6cm. Moving on to Figure B, we have two points K and L. Thus, we conclude that A is the center of the circle as it is equidistant from all points on the circle. Three of the given points are not equidistant, so E is not the circle’s center. There are two points given A and E, according to the given dataīoth the points are equidistant while we are also given that: Locating Centers – An ExampleĬonsider the following figure having two problems A and B the data is given in the figure we want to find the center of the circle and the center of the line segment.įigure 8 – Example of the Center of a Circle and Line Segment Solution This concept is illustrated in the figure below. the midpoint we will divide the distance by 2 and what we get is 2 so the midpoint (center) will on 2cm from A and 2cm from B. Let’s suppose two points A and B to find the midpoint we will calculate the distance between the two points and divide that distance into two parts.įor instance, there are two points and the distance between them is 4cm to find the center of the line segment i.e. The Center of a line segment is usually referred to as the midpoint which is basically mid of two points. Consider the below figure of an equilateral triangle the center is labeled as H where all three vertices of the triangle pass. There are many distinct points of triangles that are referred to as the center of the triangle as described below. (X – L)² + (Y – M)² + (Z – N)² =r² Center of TriangleĪn actual triangle center or triangle center in geometry is a point on a plane that, in some sense, is in the middle of the triangle, similar to the center of a square or circle. The center formula of the sphere can be written as : In a sphere, consider (L, M, N), r, and (X, Y, Z) as the coordinates of the center of the sphere, the radius of the sphere, and the coordinates of any point on the sphere respectively. The formula for finding the sphere can be expressed by the general equation for the sphere. Spheres are three-dimensional space objects formed by points that are equally distant from a point and that point is known as the center of the sphere.Ĭonsider the above figure point A is known as the center of the sphere because that point is equidistant from all the points on the surface of a sphere. The center formula of the circle can be written as : In a circle, consider (L, M), r, and (X, Y) as the coordinates of the center of the circle, the radius of the circle, and the coordinates of any point on the circle respectively. The formula for finding the center of circles can be expressed by the general equation for the circle. The reason we are calling A the center of the circle is that the distance of all the points in the circle from point A(center) is equidistant.Ĭonsider the right circle in above figure C is labeled as the Center of the circle while D, E, F, G, and H are points on the circle so all of these points will be equidistant that’s what we define above the definition of a circle and referring C as the center of the circle. Consider the figure above where a circle is drawn the point A is labeled as the center of the circle where AB is the radius with B as a point on the circle.
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