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If CD is the diameter of the circle, does y equal 60?

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by mevicks » Sat Oct 19, 2013 7:24 pm
Yvette726 wrote:If CD is the diameter of the circle, does y equal 60?

Image
(1) x = 30
(2) The length of CD is twice the length of BD.
Given: CD is the diameter
Since CD is the diameter, the angle CBD is 90°
Thus x + y + 90 = 180°
Or, x + y = 90°
If we can find either of the values x or y we can answer the question sufficiently.

Q: y = ?
Image

St1:
Directly gives the value of x, we can find y, SUFFICIENT

St2:
CD = 2 BD
But CD = 2r, thus BD = r. Now BED becomes an equilateral triangle and y = 60. SUFFICIENT
(another way to visualize this is via 30-60-90 triangle concept for right angled triangles: sides are in the ratio 1:√3:2. Since hyp = 2 CD we can conclude the angle opposite to √3 is 60 or y = 60)

Answer D
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by Uva@90 » Sat Oct 19, 2013 7:40 pm
Hi Yuvette,

As Vivek used the property of a triangle "the angle CBD is 90° "

Which can be stated as "The angle inscribed in a semicircle is always a right angle (90°).".

This property is tested on GMAT several times. I have seen many times in the same forum.(Worth remembering it)

Regards,
Uva.
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by [email protected] » Sat Oct 19, 2013 11:34 pm
Hi All,

Both medicks and Uva@90 know the "special rule" behind this question. When a triangle inscribed in a circle has a side that is the diameter of the circle, then you have a right triangle.

HOWEVER, Uva stated that the property is tested on the GMAT several times, which is simply not true. This is a rare, multi-shape geometry rule. You MIGHT see it one time on the real GMAT (although there's a pretty good chance that you won't see it at all).

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Contact Rich at [email protected]
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by mevicks » Sun Oct 20, 2013 12:18 am
Although I might agree with Rich on the rarity issue of such problems, I'd like to point out that knowing the so called "special rule" mentioned above is a MUST.

The OG math review mentions this rule (however without any concrete explanation, which is expected as it is just a review section) and we are supposed to know the before attempting geometry questions related to circles.

From pgs 134 & 135 of The Official Guide for GMAT® Review 13th Edition:
If a triangle is inscribed in a circle so that one of its sides is a diameter of the circle, then the triangle
is a right triangle.

Image

In the circle above,Image is a diameter and the measure of is Image
Similar Official Problems for practice:
OG13 DS#119
QuantReview v2 PS#162
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by Yvette726 » Sun Oct 20, 2013 6:37 am
Thank you all, i was having trouble understanding why statement 1 was sufficient. I guess it's just a rule that i have to remember.
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by theCodeToGMAT » Sun Oct 20, 2013 6:47 am
Yvette726 wrote:Thank you all, i was having trouble understanding why statement 1 was sufficient. I guess it's just a rule that i have to remember.
Yes, after all... "Know the rules well, so you can break them effectively." - Dalai Lama XIV

:)
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by mevicks » Sun Oct 20, 2013 7:34 am
theCodeToGMAT wrote: Yes, after all... "Know the rules well, so you can break them effectively." - Dalai Lama XIV

:)
lol.

let's all defeat this loch ness monster named The GMAT :D
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by theCodeToGMAT » Sun Oct 20, 2013 7:52 am
mevicks wrote:
theCodeToGMAT wrote: Yes, after all... "Know the rules well, so you can break them effectively." - Dalai Lama XIV

:)
lol.

let's all defeat this loch ness monster named The GMAT :D
Yep Mate!!!
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