How to find the length of a segment in a circle?
A segment of a circle is the region enclosed by a chord and an arc so formed touching the endpoints of the chord.
Answer: The length of the segment of the circle can be found using the intersecting chords formula, EA × EB = EC × ED.
When two chords intersect in the interior of a circle, each chord divides the circle into different parts known as the segment of the circle.
Explanation:
The following theorem tells about the relation between the four segments that are formed.
Theorem:
If two chords intersect within the interior of the circle then, the product of the length of the segments of one chord is equal to the product of the length of the segment of the other chord.
Let the two intersecting chords be AB and CD, intersecting at E as shown in the given diagram.
Circle with chords AB and CD, intersecting at E.
Therefore, EA × EB = EC × ED.
Let's take an example to understand this.
Let, EA = 3 cm, EB = 2 cm, EC = 1.5 cm, ED = ?
Let, ED = y cm.
Using, EA × EB = EC × ED
⇒ 3 × 2 = 1.5 × y
⇒ y = 6 / 1.5
⇒ y = 4
Thus, ED = 4 cm. Now, we can add this length to EC to find the length of the segment of circle CD.
CD = ED + EC
CD = 4 cm + 1.5 cm = 5.5 cm