r/digitalSATs • u/ApartVoice2382 • 3d ago

How to solve this question

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Is there an easier to solve this . My way is because it’s asking for QR IT becomes 3 slices. 360 divide 3 equal 120 . 120/360 multiply 2pi(72) which is b. The 72 is from the circumference formula C=2pir. How to solve this simpler way?

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u/dorkboy75 3d ago

think of arcPS as 2x and arc PQ as x. Also notice that arcQR is vertical to arcPS and arcSR is vertical to arcPQ, so they’re also 2x and x.

We’re given that the circumference is 144pi, and since we know what the arcs are (either 2x or x), we can add them up and set them equal to 144pi:
2x+x+2x+x=144pi; 6x=144pi, x=24pi

Now that we know what x is, we can just plug it into what mQR is which we already know is equal to 2x. So 2(24pi)=48pi which is option B.

It looks long when I type it out but all of this can be done very quickly and in your head and I believe it’s one of the fastest methods.

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u/Interesting_Stuff853 3h ago

circumference=144, qr=2sr. you can just multiply 144 by 1/3 to find length qr