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# SAT Math 2 subject test question?

In a circle of radius 5, a center angle has measure 106 degrees. What is the length of the chord joining the endpoint of the arc cut off by this angle?

*How is the answer 7.99?

### 1 Answer

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- jacob sLv 71 month agoFavorite Answer
Solution ⇒ given, θ = 106 ° radius = 5 units

Let Δ ABC,

sin( θ/2) = BC/AC = (d/2)/R

⇒ d = 2Rsin( θ/2)

d= 2 x 5 x sin(106 ° /2) =10 sin 53 °

d= 10 x 0.7986 = 7.986

DC = d = 7.99

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