Question

ABC is a right angled triangle right angled at B . A circle with centre O inscribed in the triangle . AB= 6cm and BC= 8cm . Find the radius of the circle

Answer 1

In Given Triangle ABC  

AC^2+ AB^2 = BC^2

(6*6)+(8*8)= BC^2

BC^2=64+36

BC^2=100

BC=10

Area of Triangle ABC= 8*6/2

                              =24 Cm2

Semiperemetre of ABC= (8+6+10)/2

                                 =12 cm  

Radius of circle=  Area Of Triangle /Semiperimeter of triangle

                      =  24/12

                       = 2 cm  

Hence Radius of circle is 2 cm  

Answer 2

$ab \: = 6 \: \: bc \: = 8 \\ so \: ac \: = 10 \\ so \: radius \: = \frac{ab + bc - ac}{2} \\ = \frac{6 + 8 - 10}{2} \\ = \frac{4}{2} \\ = 2$

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