a ring having radius 2 units is placed in the corner of a room such that it touches the adjecent walls. if a smaller circle is drawn in between the ring and the corner point of these two walls, what would be the area of such a circle? i dont remember the options...asked in elitmus on 10/07/2016

• when the circle is touching the wall and radius is 2 unit, then the gap between the circle and wall forms a square with side of 2 unit.... so we have to find the diagonal of the square which is D^2=2^2+2^2 =2.8284.
  so if we subtract 2.8284 -2=0.8284 ... the new circle having a diameter of 0.8284 and RADIUS will be 0.4142
  by solving we have πr2 =0.53919373
  
• 8 years agoHelpfull: Yes(8) No(10)
• no one is considering here the gap between peripheri of smaller circle and the corner point...as a matter of fact a circle cant touch corner of a wall unless its radius is zero...means a point. and yeah ...i remebered options too now...
  a) root2-1 ...which is indeed 200% wrong coz of ignoring abovesaid distance
  b) 3-2*root2 c) 6-4root2 d)7-4root 2
  now think again....
  
• 8 years agoHelpfull: Yes(6) No(0)
• answer will be pi*(6-4root2)^2
• 8 years agoHelpfull: Yes(6) No(1)
• Method1:
  Area of circle =4pi, Area of Sector of Circle =pi
  Area of square =2*2=4
  Area enclosed can be dertemined = Area of Square - area of sector .
  Method 2;
  Radius of Circle =2
  Diameter of Square =2root2
  hence diameter of small circle= 2root2- 2=0.82
  radius of circle =0.82/2=0.41
  hence area of small circle=pi *0.41*0.41=Ans
• 8 years agoHelpfull: Yes(5) No(3)
• pi*[root(2)-1]^2
• 8 years agoHelpfull: Yes(4) No(0)
• 
  2(root2 - 1)
  x= ______________
  (1 + root2)
• 8 years agoHelpfull: Yes(3) No(3)
• Draw lines from centre of ring to corner lines I.e perpendicular.
  Draw a line from centre of smaller circle to radius of bigger ring....
  It will be more clear from figure...
  Equation will be
  (2-x)^2+(2-x)^2=(2+x)^2
  Solve u will get 6-4√2
• 8 years agoHelpfull: Yes(2) No(0)
• its devastating my mind
• 8 years agoHelpfull: Yes(1) No(0)
• taking radius os small circle as r. in that case pythagores theorem will be applied where hypotenuse will be (2+r) and other two sides are (2-r) and (2-r) equate both side and solve for r you will get the solution.
• 8 years agoHelpfull: Yes(1) No(1)
• option b is correct
  
• 8 years agoHelpfull: Yes(1) No(0)
• Let r be the smaller radius and x be the gap between smaller circle and corner. Now,
  Length of diagonal of square formed due to bigger circle=2root2
  2root2= 2+2r+x (as bigger radius=2)
  further, 2(root2 -1)= 2r+x
  now apply pythagoras theorem to find the distance between center of smaller circle to corner(r+x).
  Here we get, r+x = 2(r^2)
  Now we already have 2r+x,
  So r+r+x=2(root2 -1)
  On simplifying for value of r, we get r=6-4root2
• 7 years agoHelpfull: Yes(1) No(0)
• radius of smaller circle= 2(root2-1)/2= (root2-1)
• 8 years agoHelpfull: Yes(0) No(2)
• sorry....these options are corresponding to radius of smaller circle bt i hv asked area for the same in question....so apologize fr it ...u guys solve it fr radius..
• 8 years agoHelpfull: Yes(0) No(2)
• How did u guys solve it?
• 8 years agoHelpfull: Yes(0) No(0)
• let 'a' be the radius then,
  a+a*root(2)=0.828
• 8 years agoHelpfull: Yes(0) No(1)
• In this question how can we find the side of square. There is nothing given for square side . when i found the side of the square then i will solve this question
• 8 years agoHelpfull: Yes(0) No(0)
• radius will be 6-4root2
  and area of small circle will be Pi*6-4root2
• 8 years agoHelpfull: Yes(0) No(0)
• let the radius of smaller circle 'r'.
  By applying pythagoras theorem we find the gap occur b/w wall &smaller circle [since wall act like tamgent to circle]
  
  rsqrt2+r+2=2sqrt2
  by solving this we get r=6-4sqrt2
• 8 years agoHelpfull: Yes(0) No(0)
• distance from corner point to peripheri= 2*root2-2
  radius of smaller circle= 2*(root2-1)/root2+1
  area =pi*r2
• 8 years agoHelpfull: Yes(0) No(0)
• π4((3-2√2)/(3+2√2))
• 7 years agoHelpfull: Yes(0) No(0)
• radius is 3-2root(2)
  area is {17-12root(2)}*3.14
• 7 years agoHelpfull: Yes(0) No(0)
• let dia of smaller circle be =d
  length of diagonal from the centre of the bigger circle to the corner of the wall= sqrt(8).
  distance from the corner to the tip of smaller circle = a.
  using similarity,
  2/sqrt(8)=d/2/(d/2+a).......(2)
  a = sqrt(8) - d - 2...............(1)
  solving the eqn. we will get the value of d, and hence the area.
• 6 years agoHelpfull: Yes(0) No(0)