Among the infinitely many possible forms in the universe, perhaps the circle is the most alluring. So much so that even the celestial powers chose the shape of a sphere for nearly all celestial bodies, which are nearly circular. So it was natural for mankind to spend a lot of time studying the properties of circular shapes, and you can learn about them all by visiting Cuemath online. Also, not just the shape of the planets and stars but also the path along which they travel is nearly circular.
Before diving into the chord of a circle, let us begin with the circle itself, which is perhaps the simplest of shapes with no vertices or edges, made of one smooth curved line which goes around a fixed point called the center of the circle and all points on the circle are always equidistant from the center point. The size of the circle depends on how far the periphery of the circle is from the center of the circle. The larger the distance, the larger the circle. The distance from the center of the circle to any point on the periphery of the circle is called the radius of the circle and is always the same size no matter what point we pick on the circle’s periphery.
Another measure of the circle is twice the radius, also known as the diameter, any diameter, when drawn on a circle divides the circle in exactly two equal halves, and diameter connects two points on the circle while also passing through the center. It is worth noting that in the early times, mathematicians were able to establish that the length of the circle divided by the diameter of the circle always gave a fixed value of 22/7; this constant, better known as pi thereafter, was found to be of significant utility.
A circle has many elements to it based on where a line is drawn onto it. If a line is drawn such that it touches the circle at exactly one point, then such a line is called a tangent to the circle, and if we draw a radius to the point of contact, then the line of radius and the tangent would be perpendicular to each other. If the line cuts the circle at two points and also passes through the center of the circle, then such a line is called the diameter, and it cuts the circle in exactly two equal halves.
But what about when a line cuts the circle in two points, but it does not pass through the center of the circle, so it is not a diameter. Well, in such a case, we would have two parts to the circle, a smaller part and the bigger one. So such a line that cuts the circle in two points is called a chord, and when it passes through the center, it has a special name of diameter. So, we can say diameter is the biggest chord possible.
If we have two chords whose distance from the center of the circle is the same, then the length of the two chords would be the same too; also the vice versa is true, that is, if there are two chords of the same length in a circle then their distance from the center of the circle is the same.
Often the technique used to find the length of the chord is to draw a triangle by connecting the two intersection points of the chord and the circle with the center of the circle. Thus we get an isosceles triangle with two sides of equal length, same as the radius of the circle, and then using trigonometry, one can find out the length of the chord if the angle made by the two radius lines is known.
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