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21 Jul 2022, 08:00
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Two circles are inscribed in a rectangle, as shown above. What is the distance between the centers of these circles?
A. 2
B. \(\sqrt{5}\)
C. 3
D. \(\sqrt{10}\)
E. \(2\sqrt{5}\)
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21 Jul 2022, 08:05
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Bunuel
The diameter of each circle is 2. If the two circles were side-by-side and tangential, their centers would be separated by 2r = d= 2. But they are offset a bit vertically, so their centers are farther apart than 2. A is out. Do we want something a little more than 2 or a lot more than 2? Just a little. Certainly not more than 1.5x. C, D, and E are out.
Answer choice B.
21 Jul 2022, 08:17
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the value of digonal is 3^2+4^2 ; √25 ; 5
area of the half of the rectangle 3*4/2 ; 6
let xy be the distance of two center circle
xy = √( 3-2r)^2 + ( 4-2r)^2
we can say three ∆ area
3r/2 + 4r/2 + 5r/2
12r/2 ; 6r
6r=6
r=1
substitute r in √( 3-2r)^2 + ( 4-2r)^2
xy = √(1+4) ; √5
OPTION B \(\sqrt{5}\)
area of the half of the rectangle 3*4/2 ; 6
let xy be the distance of two center circle
xy = √( 3-2r)^2 + ( 4-2r)^2
we can say three ∆ area
3r/2 + 4r/2 + 5r/2
12r/2 ; 6r
6r=6
r=1
substitute r in √( 3-2r)^2 + ( 4-2r)^2
xy = √(1+4) ; √5
OPTION B \(\sqrt{5}\)
Bunuel
