A circle is inscribed in a given square and another circle is circumscribed about the square. what is the ratio of the area of the inscribed circle to that of the circumscribed circle?
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if a circle is inscribed in the square then the diameter of the circle is equal to side of the square.
assume side of the square as a. then radius of circle= 1/2a.
area of circle inside circle= π(a/2)^2=1/4(πa^2)
if a square is circumscribed by circle then diagonal of square is equal to diameter of circle.
diagonal of square=√2a
radius of circle =√2a/2
area of outer circle =π(√2a/2)^2 = 1/2(πa^2)
ratio= > 1/4(πa^2)=1/2(πa^2)
finally Ratio=1:2
assume side of the square as a. then radius of circle= 1/2a.
area of circle inside circle= π(a/2)^2=1/4(πa^2)
if a square is circumscribed by circle then diagonal of square is equal to diameter of circle.
diagonal of square=√2a
radius of circle =√2a/2
area of outer circle =π(√2a/2)^2 = 1/2(πa^2)
ratio= > 1/4(πa^2)=1/2(πa^2)
finally Ratio=1:2
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7
Answer:
ratio is 1:2
the ratio of area of inscribed circle:the ratio of area of circumscribed circle is
1:2
it is the answer
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