How do you find the length of the chord of a circle with radius 8 cm and a central angle of 110^@?

1 Answer
MeneerNask
Jan 9, 2015

You first draw a triangle connecting the ends of the chord (A and B) and the centre of the circle C.
You'll learn more if you make a drawing or scetch now.

Then you divide the chord in two equal halves and connect the middle M to the centre of the circle. You will see that you now have two equal (mirrored) triangles. It's easy to see (and prove) that both are rectangular at M.

Let's consider triangle AMC.
We know that the angle at M is now half of 110^0=55^0
And we know that AC=8 cm

sin /_M=(AM)/(AC)->sin 55^0=(AM)/8->AM=8*sin55^0

AM=8*0.819...~~6.55 cm.

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