BTGmoderatorDC wrote:In a circle centered on point O with radius 8, diameter AC and point B on the circle, pictured above, what is the length of line segment (AB)?

(1) ∠AOB = 120°
(2) OB = BC

OA D

Source: Veritas Prep

The image is not attached.

Anyway, it's not needed.

So, B is any random point on the circle. Draw the figure as per the given information.

We have to get the value of AB.

Let's take each statement one by one.

(1) ∠AOB = 120°

Join OB. In ∆AOB, we have OB and AO as radii. Thus, AO = OB = 8/2 = 4. Thus, ∆AOB is an isosceles triangle. Thus, /_OAB = /_OBA. Given /_AOB = 120º, we have /_OAB = /_OBA = 30º. The length of AB can be calculated by splitting ∆AOB into two equal triangles of 90-60-30. We know that for a 90-60-30 triangle if the length of one side is known, we can get the value of all the sides. Sufficient.

(2) OB = BC

Join OB. We know that OB is radius; thus, OB = OC = 4. And, OC = OB = BC = 4; so, ∆OBC is an equilateral triangle. Thus, /_BOC = 60º, thereby /_AOB = 180 - 60 = 120º.

This is the same information that we got in Statement 1. Sufficient.

The correct answer: D

Hope this helps!

-Jay
_________________
Manhattan Review GRE Prep

Locations: GRE Classes Miami | GRE Prep Course Munich | GRE Prep Denver | LSAT Prep Course Orlando | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.