Latest Elitmus Aptitude Question SOLUTION: The diameter of a Circle is 18 cm , triangle is inscribed inside the circle . another circle in inscribed in that triangle whose radius in 6 cm. find the perameter of the triangle.

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(#M40037825) ELITMUS Category question asked in 20 july exam Keep an EYE

The diameter of a Circle is 18 cm , triangle is inscribed inside the circle . another circle in inscribed in that triangle whose radius in 6 cm. find the perameter of the triangle.

Asked In Elitmus Gaurav Malhotra (9 years ago)

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RAKESH  (9 years ago)

if diameter of the circle being largest side of the right angled triangle
then let two sides of triangle be x,y

1/2 *xy = (x+y+18)/2 * 6
=> xy = 6(x+y) + 108

x^2 + y^2 = 18^2
=> (x+y)^2 - 2xy - 324 = 0
=> (x+y)^2 - 12(x+y) - 216 - 324 = 0
=> (x+y)^2 - 12(x+y) - 540 = 0
=> (x+y-30)(x+y+18)= 0
=> (x+y)= 30
perimeter = x+y+18 = 30 + 18 = 48

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Vivek singh bhatnagar  (9 years ago)

if diameter of the circle being largest side of the right angled triangle.
in triangle ABC,B is right angle
R=9cm
r=6cm
circumradius (R) = Hypotenuse/2
R=AC/2
9=AC/2
AC=18cm
r=(AB+BC-AC)/2
6=(AB+BC-18)/2
AB+BC=30
s=(AB+BC+AC)/2
perimeter = 2s
......perimeter of the triangle = 42.

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Mukesh Nayal  (9 years ago)

i think the smaller circle should have diameter as 6 not radius ,
If such is the case then answer is 54

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Chandrashekhar   (9 years ago)

Question slight modification there..diameter of the circle being largest side of the right angled triangle...

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