<Tri-2023-2029>, hint

Let inradius,r, circumradius, R. of triangle ABC  

Draw a circle of radius R, BC=2R. A lie on the circle . Height AH=h

1>. b+c=2R-2r. 2>. bc =2R h 3>.(2R) square=b square x c square. From 1>,2>,3> h=2r+(r x r)/R.

Draw a semicircle of radius R and a line g parallel to BC ,distance AH= h from BC.