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# In the figure above, the radius of circle with center O is 1

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Manager
Joined: 15 Sep 2016
Posts: 71
Location: Pakistan
Concentration: Finance, Technology
Schools: CBS '20
GMAT 1: 640 Q43 V35
In the figure above, the radius of circle with center O is 1  [#permalink]

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28 Jul 2018, 01:15
Hi Everyone,

Thanks for the very useful discussion here. I understood the property of diameter being the hypotenuse.
Please excuse my asking this extremely basic question (it must be a forgotten property), how do we know if the base is AB or BC?

Also, a super basic question for my learning.
Why are we taking hypotenuse = 1
Diameter is 2(r) = 2
Shouldn't we take:

1/2 *b*h
= 1/2 *sqrt(3) *2
= sqrt(3)

Thanks!
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If you must err, err on the side of hope.
Math Expert
Joined: 02 Sep 2009
Posts: 55635
Re: In the figure above, the radius of circle with center O is 1  [#permalink]

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28 Jul 2018, 05:19
KungFuGmat wrote:
Hi Everyone,

Thanks for the very useful discussion here. I understood the property of diameter being the hypotenuse.
Please excuse my asking this extremely basic question (it must be a forgotten property), how do we know if the base is AB or BC?

Also, a super basic question for my learning.
Why are we taking hypotenuse = 1
Diameter is 2(r) = 2
Shouldn't we take:

1/2 *b*h
= 1/2 *sqrt(3) *2
= sqrt(3)

Thanks!

Your second doubt is not clear. The radius = 1, so the diameter, AC, which is also the hypotenuse is 2.
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Math Expert
Joined: 02 Sep 2009
Posts: 55635
Re: In the figure above, the radius of circle with center O is 1  [#permalink]

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28 Jul 2018, 05:20
KungFuGmat wrote:
Hi Everyone,

Thanks for the very useful discussion here. I understood the property of diameter being the hypotenuse.
Please excuse my asking this extremely basic question (it must be a forgotten property), how do we know if the base is AB or BC?

Also, a super basic question for my learning.
Why are we taking hypotenuse = 1
Diameter is 2(r) = 2
Shouldn't we take:

1/2 *b*h
= 1/2 *sqrt(3) *2
= sqrt(3)

Thanks!

Your first doubt is addressed here: https://gmatclub.com/forum/in-the-figur ... l#p1803640 and here: https://gmatclub.com/forum/in-the-figur ... l#p2097597

Your second doubt is not clear. The radius = 1, so the diameter, AC, which is also the hypotenuse is 2.
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Joined: 20 Aug 2018
Posts: 26
In the figure above, the radius of circle with center O is 1  [#permalink]

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24 Nov 2018, 17:06
A video explanation can be found here:

Three of the many equations and facts you'll need to memorize for the GMAT are

- Area of a triangle = 1/2(base)(height)

- In a right triangle with angles 30-60-90 degrees, if the leg opposite the 30 degree angle has length a, then the hypotenuse has a length of 2a, and the other leg has a length of a√3 (see video below)

- If a triangle inscribed in a circle has the diameter of the circle as one of its sides, that side will always be the hypotenuse, and the two legs that touch the circumference of the crcle will always interesect at 90 degrees (also best explained in video below)

Here we have hypotenuse = 2, therefore base = 1 and height = √3, therefore area = 1/2(1)(√3) = √3/2

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In the figure above, the radius of circle with center O is 1   [#permalink] 24 Nov 2018, 17:06

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