Geometry Question Bank #16

[cssears]

Rectangle ABCD is inscribed in circle P. What is the area of circle P?

(1) The area of rectangle ABCD is 100.

(2) Rectangle ABCD is a square.

Why is statement 1 not sufficient?

[akhp77]

Statement 1:
Let side of rectangle be 2a and 2b
2a * 2b = 100
ab = 25 = 1*25 = 5*5 = 2.5 * 10
radius r = sqrt(a*a + b*b)
so r can take several values
No Sufficient

Statement 2:
let x be the side of square but area is not given
So Not sufficient

Statement 1 & 2
x * x = 100; x = 10
r = (10/2) * sqrt(2)

So Sufficient

Ans: C

[StaceyKoprince]

As akhp77 said, there are multiple possible dimensions for a rectangle with an area of 100. Different dimensions would result in different radii for circle P.

For example, the rectangle might have dimensions 10x10. It might also have dimensions of 5x20. cssears, work out both scenarios from there to see how circle P would have a different radius in each case. Let us know if you have any more questions.