The circle inscribed in the triangle ABC touches the side BC, CA and AB in the point `A_(1)B_(1) and C_(1)` respectively. Similarly the circle inscribed in the `Delta A_(1) B_(1) C_(1)` touches the sieds in `A_(2), B_(2), C_(2)` respectively and so on. If `A_(n) B_(n) C_(n)` be the nth `Delta` so formed, prove that its angle are
`pi/3-(2)^-n(A-(pi)/(3)), pi/3-(2)^-n(B-(pi)/(3)),pi/3-(2)^-n(C-(pi)/(3)).` Hence prove that the triangle so formed is ultimately equilateral.

Answer

`A_(n)=B_(n)=C_(n)=pi/3.`