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C
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Difficulty:
45%
(medium)
Question Stats:
70% (02:37) correct
30%
(03:02)
wrong
based on 33
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In the figure, AB = BC and the area of the shaded region is \(π + 2\) square meters. What is the radius of the circle in meters?
A. \(\frac{\sqrt{2}}{2}\)
B. 1
C. \(\sqrt{2}\)
D. 2
E. 4
Attachment:
1.png [ 13.55 KiB | Viewed 1909 times ]
asishron29181
Joined: 04 May 2020
Last visit: 04 Nov 2022
Posts: 185
Given Kudos: 68
Location: India
Schools: Great Lakes (I)
GMAT 1: 610 Q47 V27
WE:Programming (Computer Software)
18 Jun 2021, 03:17
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Given, AB = BC
Area of the shaded region is π+2
Area of shaded region = Area of semicircle + Area of triangle ABC
Area of triangle, given AB = BC is 0.5 * b * h = 0.5*x*x = 2
x^2 = 4
x= 2
In a 45-45-90 triangle, side corresponding to the angles are = x:x: √2 x
So the diameter of the circle turns out to be = √2 x = 2√2
Radius of the circle = √2
Area of semicircle = π* r^2 / 2
Given π* r^2 / 2 = π
r^2 =2
r = √2
IMO C
Area of the shaded region is π+2
Area of shaded region = Area of semicircle + Area of triangle ABC
Area of triangle, given AB = BC is 0.5 * b * h = 0.5*x*x = 2
x^2 = 4
x= 2
In a 45-45-90 triangle, side corresponding to the angles are = x:x: √2 x
So the diameter of the circle turns out to be = √2 x = 2√2
Radius of the circle = √2
Area of semicircle = π* r^2 / 2
Given π* r^2 / 2 = π
r^2 =2
r = √2
IMO C
18 Jun 2021, 03:23
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AC is the diameter = say equal to 2r
Area of shaded region = area of triangle ABC +Area of semicircle of radius r
Area of triangle ABC = 1/2 *2r*r
Area of semicircle =Pi* \(r^2\)/2
Pi + 2= Pi * \(r^2 \)/2 + \(r^2\)
\(r^2\) = 2
r = \(\sqrt{2}\) r can not be negative
C is the answer
Area of shaded region = area of triangle ABC +Area of semicircle of radius r
Area of triangle ABC = 1/2 *2r*r
Area of semicircle =Pi* \(r^2\)/2
Pi + 2= Pi * \(r^2 \)/2 + \(r^2\)
\(r^2\) = 2
r = \(\sqrt{2}\) r can not be negative
C is the answer
Bunuel
