Bunuel wrote:
What is the circumference of circle O?
(1) The circle inscribes a square.
(2) The perimeter of the square is 10.
Statement 1) Circle inscribes a square - tells us that the square is inside the circle ..
Insufficient. Rule out Choice A) & D)
Statement 2) Perimeter of square is 10, let 's' be the length of each side of the square => 4s = 10 => s=2.5
But we have no relation of the square with the circle.
Square may be inscribed or the circle inscribes the square. The side 's' as tangent to the circle.
Insufficient Rule out Choice B)
Statement 1) & 2) together - Circle inscribes a square and each side of square is 2.5units.
Rule of geometry - when a circle inscribes a square. the diagonals of the square intersect at right angle at the center point of the circle.Hence using the pythagoras theorem, one can find the radius 'r' of the circle => r^2+r^2=2.5^2
From this we can find 'r' and calculate the circumference = 2 x pie x r.
Choice C) is the answer
Statement 1) & 2) together are sufficient to ans the question.Good luck
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