Latest Infosys Aptitude Question SOLUTION: 16. Find the radius of the circle inscribed in a triangle ABC. I. Triangle ABC is a right-angled isosceles triangle with the hypotenuse as 62 cm.

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16. Find the radius of the circle inscribed in a triangle ABC.
I. Triangle ABC is a right-angled isosceles triangle with the hypotenuse as 62 cm.

Asked In Infosys Shilpi Shandilya (9 years ago)

Solved Abhishek Dey Read Solution (3)

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Abhishek Dey  (9 years ago) Best Solution

Since hypotenuse is 6 root 2 cm. Sides are 6 cm each as it is an isosceles triangle. Now, if we have an inscribed circle the property is the point where the circle touches the sides are exactly 2/3 rd of the length of sides, i.e, 2/3*6=4cm. Now, if you drop 2 radii on the sides of triangle then they act as perpendiculars on sides. So, it forms a small square of (6-4)=2 cm each side. Thus, radius of the circle is 2 cm.

Is this solution Helpfull? Yes (15) | No (3)  

Roop Raushan  (9 years ago)

Answer will be 6 - 3 root(2)= 1.8 (approx)
1. very easy to find other sides are 6 cm then apply
now join each vertex with center of circle we get three small triangle its center are equidistant from side as given inscribed i.e., r
then equation as
1/2*r*6 + 1/2*r*6 + 1/2*r*6root(2)= 1/2*6*6
solve this and get 6- 3root(2) cm

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Pallavi Rai  (9 years ago)

Inradius = area /semiperimeter

sides are 3root2,3root2,36
inradius= 1/2*3root 2* 3root2=9
semiperimeter=3(root 2 +6)
inradius=3/(root 2+6)

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