Converging Points

Geometry Level 2

{An+1=αAn+(1α)BnBn+1=αBn+(1α)CnCn+1=αCn+(1α)An \large {\left\{\begin{matrix}A_{n+1}=\alpha A_n+(1-\alpha)B_n \\ B_{n+1}=\alpha B_n+(1-\alpha)C_n \\ C_{n+1}=\alpha C_n+(1-\alpha)A_n\end{matrix}\right.}

Let A1,B1,C1A_1,B_1,C_1 be three distinct non-collinear points on the coordinate plane.
Also An,Bn,CnA_n,B_n,C_n satisfy the recurrence relation above (0<α<10<\alpha<1).

Then limnAn\displaystyle\lim_{n\to\infty}A_n is the __________\text{\_\_\_\_\_\_\_\_\_\_} of the triangle A1B1C1A_1B_1C_1.

×

Problem Loading...

Note Loading...

Set Loading...