Let A B C D be a quadrilateral with area 18 , with side A B parallel to the side C D and A B=2 C D . Let A D be perpendicular to A B and C D . If a circle is drawn inside the quadrilateral A B C D touching all the sides, then its radius is

Step-by-step solution

18= 1 2 (3 )(2 r) r=6 Line, y=- 2 r (x-2 ) is tangent to circle aligned (x-r)^2+(y-r)^2 & =r^2 2 & =3 r and =6 r & =2 aligned aligned 1 2 (x+2 x) 2 r & =18 x r & =6 & = x-r r (90^ - ) & = 2 x-r r x-r r & = r 2 x-r (2 x-3 r)=0 aligned x= 3 r 2 From Eqs. (i) and (ii), we get r=2