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.

• 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.
• 9 years agoHelpfull: Yes(15) No(3)
• 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
• 9 years agoHelpfull: Yes(4) No(2)
• 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)
• 9 years agoHelpfull: Yes(1) No(5)