Math CentralQuandaries & Queries


Question from Arwin:

The radius of a circle is 17 cm. A chord XY lies 9 cm from the centre and divides the circle into two segments. Find the perimeter of the minor segment.

Hi Arwin,


In my diagram $M$ is the center of the circle. The minor segment is shaded blue and its perimeter is composed of two section, the chord and the arc of the circle from $X$ to $Y.$

The angle $XMC$ is a right angle (do you see why?) so Pythagoras Theorem allows you to find the distance from $X$ to $M.$ and hence the length of the chord $XY.$ The length of the arc from $X$ to $Y$ can be found using the information in Harley's response to an earlier question. Make sure you have you calculator set to radians rather than degrees.


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