VerifiedHint: A chord of a circle is defined as the line segment joining any two points on the circumference of the circle, passing through its interior. The length of the chord can vary according to the distance between those two points.
Complete step-by-step answer:
AB is an arbitrary chord of the circle.
In order to find the longest chord, we need to find the two points on the circumference having the maximum distance between them. When we observe the figure closely, we can see that-
We can see that X and Y are the farthest points on the circumference of the circle, and they pass through its centre. This implies that XY is the diameter of the circle. Therefore, the longest chord of the circle is its diameter.
We have been given the radius of the circle as 2.9 cm.
We know that the diameter $d = 2r$, so
d = 2(2.9) = 5.8 cm
This is the required answer.
Note: The answer obtained in this question can be used as a result. That is, the diameter is always the longest chord of a given circle. Also, we should take care of the units in this question, because it has been specifically asked to give the answer in centimeters.
