There is a right angle triangle inside a circle of diameter 18cm. Inside this triangle ,there is another circle of diameter 6 cm. Find the perimeter of the triangle.
OPTIONS:
A.)24cm B.)36*2^1/2cm C.)36cm D)54cm

• For more illustration see the Wikipedia page of Right Angle Triangle...
  Some Rules:-
  1)The radius of the incircle of a right triangle with legs a and b and hypotenuse c is r=(a+b-c)/2
  2)The radius of the circumcircle is half the length of the hypotenuse R=c/2
  3)Thus the sum of the circumradius and the inradius is half the sum of the legs R+r=(a+b)/2
  
  From 2nd Rule c=18cm
  From 3rd Rule a+b= 2*(9+3) =24cm
  Hence Perimeter a+b+c= 24+18= 42 cm Ans.
  Now, I am not sure with the option you provided and there's confusion with option b).. but clearly a,c and d are not correct
• 9 years agoHelpfull: Yes(10) No(1)
• 42 is the correct answer , It was mentioned in the option .
• 9 years agoHelpfull: Yes(4) No(0)
• Answer is 42cm.
  If you'll draw the fig.
  u'll find hypotenuse of right angle triangle is 18.
  hypotenuse can be divided in two parts: Let one is 'x' then other will be '18-x'(where it is touching the circle).
  and when u'll apply the properties of tangent(perpendicular to radius), square and right angle triangle.
  Let triangle have sides a, b and c(hypotenuse).
  c=18.
  a=18-x+3.
  b=x+3.
  perimeter= 18+18-x+3+x+3= 42.
  so 42 is answer.
  
• 9 years agoHelpfull: Yes(3) No(0)
• Logically for a right angle triangle with sides a, b, c b as hyp a+c>b... So option 24 and 36 is not possible... 54 means 18+18+18(as no side can be>18) which is also not possible.... So only possible answer... 36√2
• 9 years agoHelpfull: Yes(2) No(3)
• 36*2^1/2 ans
• 9 years agoHelpfull: Yes(0) No(3)
• b is the right ans
  
• 9 years agoHelpfull: Yes(0) No(0)
• its 54 cm....
  1) Area of triangle= (a*b*c)/4R..... where R is circumradius
  2)Area of triangle=S*r ...................where r is inradius and S is semiperimeter of the given triangle and it
  is (a+b+c)/2...... where a,b,c are the sides of triangle
  3) the area will be same because these are the area of same triangle
  So equate these two........
  we will get (a+b+c)=a*b/3
  4) from Pythagoras theorem we will get a^2+b^2=18^2
  and a*b= 9*18
  5) from 3rd (a+b+c)=9*18/3..... which is equal to 54..:)
• 9 years agoHelpfull: Yes(0) No(1)