CD is diameter

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jain2016: Master | Next Rank: 500 Posts; Posts: 313; Joined: Tue Oct 13, 2015 7:01 am; Thanked: 2 times

CD is diameter

by jain2016 » Wed Feb 24, 2016 9:20 am

If CD is the diameter of the circle, does x equal 30?

(1) The length of CD is twice the length of BD.

(2) y = 60

Hi Experts ,

Please explain only statement 2.

Thanks,

SJ

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Source: Beat The GMAT — Data Sufficiency | Wed Feb 24, 2016 9:20 am

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by [email protected] » Wed Feb 24, 2016 10:07 am

Hi jain2016,

This question is based on a relatively rare Geometry rule involving triangles inside of circles:

IF... all the 3 points of the triangle are on the circumference of the circle AND one side of the triangle is the diameter of the circle, then the triangle is a RIGHT TRIANGLE (the angle that is not on the diameter is the 90-degree angle).

So, when you factor in the information in Fact 2 - that y=60, and you know that angle B=90, then you know that x=30 and the answer to the question is ALWAYS YES. Thus, Fact 2 is SUFFICIENT.

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