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

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AAPL: Moderator; Posts: 2632; Joined: Sun Oct 29, 2017 2:08 pmFollowed by: 2 members

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 160Â°, and minor arc BD is 140Â°. If B bisects minor arc AC, then what is the measure of minor arc AD?

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

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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Source: Beat The GMAT — Problem Solving | Sat Nov 18, 2017 3:02 pm

EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pmFollowed by: 12 members; Thanked: 180 times

by EconomistGMATTutor » Sun Nov 19, 2017 9:34 am

Hello AAPL.

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

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

As BD=140Âº and BC=80Âº, then CD=60Âº.

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

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

So, the correct answer is C .

I hope this may help you.

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

Regards.

GMAT Prep From The Economist
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