Question

∆Lmn is a right angled triangle with angle l=90°.A circle inscribed in it . the length of the sides containing the right angled are 6cm and 8cm .find the radius of the circle​

Answer 1

The radius of the circle is 2 cm

1  LMN is  a right angled triangle and a circle is inscribed in it

2  let LM=6 cm and LN= 8cm

3 By Pythagoras theorem

          $MN^{2}=LM^{2}+LN^{2}$

                    $=6^{2}+8^{2}$

                    =36+64

                    =100

           MN=10 cm

 4  Area of the triangle= $\frac{1}{2}$ x base x height

                                  =  $\frac{(6)(8)}{2\\}$

                                  =24 $cm^{2}$

5  Semi perimeter of triangle LMN = $\frac{(L+M+N)}{2}$

                                                       =6+8+10/2

                                                        =24/2

                                                         =12 cm

6  Radius of the circle= Area of the triangle/semi perimeter of the triangle

                                    = 24/12

                                   = 2 cm