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Points A, B, C, D lie in this order on the circumference...

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by AAPL » Sat Nov 18, 2017 3:02 pm
Points A, B, C, D lie in this order on the circumference of a circle. Minor arc AC is 160°, and minor arc BD is 140°. If B bisects minor arc AC, then what is the measure of minor arc AD?

A. 80°
B. 120°
C. 140°
D. 160°
E. 220°

The OA is C.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.
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by EconomistGMATTutor » Sun Nov 19, 2017 9:34 am
Image

Hello AAPL.

If you look at the image and fill it with the data, you will get the correct answer.

The measure of AC=160º and B bisects this arc, so AB=80º and BC=80.

As BD=140º and BC=80º, then CD=60º.

So, the meause of AD is AC+CD=160º+60º=220º.

Then, the minor arc AD is 360º-220º=140º.

So, the correct answer is C .

I hope this may help you.

I'm available if you'd like a follow up.

Regards.
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