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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