How to find the length of a line segment in a circle?

Line segments are a very important part of geometry. Line segments make polygons and can also be used to represent equations on graphs. They have interesting properties which are to be learned in order to do well in geometry exams! Let's learn how to find the length of a line segment in a circle, which can also be called chords.

Answer: To find the length of a line segment in a circle, we can use the formula d = 2r sin(t/2), where r is the radius of the circle and t is the angle between the radii.

Let's understand in depth.

Explanation:

In the above figure, we have a circle with a radius r. The angle between the radii is given to be t.

We can use the formula d = 2r sin(t/2) to find the length of the chord d.

Let's take an example:

Let us assume r = 10 and t = 90°. This is an angle subtended by a quarter of a circle.

Hence, using the formula above, we get d = 2r sin (90/2) = 2r × 1/√2 = √2r = 10√2.

Now, let r = 10 and t = 180°. This is the angle subtended by a semi-circle.

Hence, using the formula above, we get d = 2r sin (180/2) = 2r × 1 = 2r = 20, which is the diameter of the circle!

Hence, to find the length of a line segment in a circle, we can use the formula d = 2r sin(t/2), where r is the radius of the circle and t is the angle between the radii.