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# If a circle of area 2π is circumscribed around an isosceles right tria

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If a circle of area 2π is circumscribed around an isosceles right tria  [#permalink]

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09 May 2015, 01:48
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93% (01:26) correct 7% (04:36) wrong based on 46 sessions

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If a circle of area 2π is circumscribed around an isosceles right triangle, what is the area of the triangle?

A. √2
B. 2
C. 2√2
D. π
E. π·√2
Veritas Prep GMAT Instructor
Joined: 23 Oct 2013
Posts: 144
If a circle of area 2π is circumscribed around an isosceles right tria  [#permalink]

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10 May 2015, 17:56
2
90 degree triangles that are inscribed in a circle always have end points that are at either end of the circle's diameter. This is true because of the inscribed angle rule of circles (double an inscribed angle and treat it as a central angle). Therefore if the inscribed triangle has a 90 degree angle such as this one, then it is covering 180 degrees of the circle, and therefore its base spans the diameter.

Because the circle's area is 2*pie, and the area of a circle = pie*r^2, then we know that the radius of the circle is sqrt2. Given this, we know that the triangle's base (the diameter) is 2*sqrt2, and its height (which is just the radius) is sqrt2. Therefore, the area of the triangle = 1/2*b*h = 1/2*2*sqrt2*sqrt2 = 2, yielding answer choice B.

I hope this helps!
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Re: If a circle of area 2π is circumscribed around an isosceles right tria  [#permalink]

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11 May 2015, 03:16
1
reto wrote:
Attachment:
T6337.png
If a circle of area 2π is circumscribed around an isosceles right triangle, what is the area of the triangle?

A. √2
B. 2
C. 2√2
D. π
E. π·√2

The area of the triangle is less than half (π = ~3.14) and more than fourth(π/2 = ~1.57) of that of the circle. Only B fits.

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Re: If a circle of area 2π is circumscribed around an isosceles right tria   [#permalink] 11 May 2015, 03:16
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