Math CentralQuandaries & Queries


Question from Dale:

How do I find the central angle if I only have the cord length and radius.

Hi Dale,

What you have is an isosceles triangle and you know the lengths of the three sides. Join the vertex C to the midpoint M of the base.


If the radius is r and the length of the chord is c then triangle CMB is a right triangle with |BC| = r and |MB| = c/2. Hence the sine of the angle BCM is (c/2)/r = c/(2r). Hence the central angle BCA has measure

2 sin-1[c/(2r)]

I hope this helps,

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