A semicircle is drawn with AB as its diameter. From C, a point on AB, a line perpendicular to AB is drawn, meeting the circumference of the semicircle at D. Given that AC=2cm and CD=6cm, the area of the semicircle in square cm will be ?

• let O be center of circle and radius be x.
  C can be anywhere on AB.Let us suppose that C is somewhere between A and O.
  AC=2cm....so CO=(x-2)
  DO=x,CD=6cm
  CDO form a right angled triangle with right angle at C.
  Using Pythagoras theorem,
  x^2=6^2+(x-2)^2
  4x=40
  x=10cm
  area=[pi(x)^2]/2
  area=50pi
  
  
  
• 10 years agoHelpfull: Yes(110) No(3)
• Ans is:50pi
  First draw a Diagram
  AC/CD=CD/BC
  CD^2=AC.BC
  6^2=2X
  36=2X
  X=18
  AB=AC+CB
  AB=2+18=20
  RADIOS OF CIRCLE=20/2=10
  AREA=1/2*pi*r^2
  =1/2*pi*10^2
  =100/2*pi
  =50pi is Ans...
• 10 years agoHelpfull: Yes(42) No(2)
• ANS: 50pi; (where pi=3.14)
  
  diameter AB=AC+CD;
  let CD=x;
  AC is altitude on AB
  and we know that in semi-circle wherever point D is doesn't matter it will make right angle-triangle
  Now: AC= 2cm
  CD=6cm
  so
• 10 years agoHelpfull: Yes(4) No(6)
• sry the answer is 50pi because it is semicircle....i did for circle
  
• 10 years agoHelpfull: Yes(3) No(3)
• Triangle ACD and triangle BCD are similar triangles so
  AC/DC=DC/BC
  2/6=6/BC
  BC=18
  Diameter D=AC+BC=2+18=20; r=10
  Area of semicircle= pi* 10^2/2=50*pi
  
• 9 years agoHelpfull: Yes(3) No(0)
• 2*(d-2)=6*6
  d=20
  area=100pi sq.cm
• 10 years agoHelpfull: Yes(2) No(4)
• Triangle ADB forms a right angled triangle.
  DC becomes the altitude of triangle ADB.
  we have that DC^2=AC*CB, from that we can find the length of BC as 18 cm.
  Therefore diameter of the semicircle AB = AC+CB = 2+18 = 20 cm => radius = 10 cm.
  Area of the semicircle=( pi*(10^2))/2
  =50 *pi sq.cm
  
  
  
  
• 9 years agoHelpfull: Yes(1) No(1)
• trial and error method
  subham from AOT
  this is semicircle so area will be area of cicle divide by 2
  now area of semi ciclle is (Pi*r^2)/2
  leave pi this is common in option
  so r square then divide by two
  now multiply every option by 2 we get 100,110,62,164 by seeing them u find that only first option is square of some integer avalue i.e 10 so r is 10 and answer is 50pi
  easy isn't it.
• 7 years agoHelpfull: Yes(1) No(0)
• its 50π
  the remaining diameter can be found by pythagores theorem
• 10 years agoHelpfull: Yes(0) No(1)