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If a smaller circle is inscribed in an equilateral triangle

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by Max@Math Revolution » Wed Mar 02, 2016 10:00 pm
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If a smaller circle is inscribed in an equilateral triangle and a lager circle circumscribed about the triangle shown as above figure, what is the ratio of the lager circle's area to the smaller circle's area?

A. 1:2
B. 1:√3
C. 1:3
D. 1:4
E. 1:5


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by Dario@VinciaPrep » Thu Mar 03, 2016 1:49 am
D, as the ratio between the two radius is 2 (property of equilateral triangle)
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by Max@Math Revolution » Sun Mar 06, 2016 2:39 am
If a smaller circle is inscribed in an equilateral triangle and a lager circle circumscribed about the triangle shown as above figure, what is the ratio of the lager circle's area to the smaller circle's area?

A. 1:2
B. 1:√3
C. 1:3
D. 1:4
E. 1:5


-> In the above picture, angle A=90 degrees and ABO=30 degrees, which makes AO:BO=1:2. Since ratio of area=the square of ratio of length, it is (1:2)^2=(1/2)^2=1/4=1:4. Thus, D is the answer.
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