We can simplify the circuit as follows.

We can replace the branch having 100k and 20k resistance with a resistance and a source of some potential. 100k and 20k resistances are in parallel if we short all the voltage sources. Hence, the equivalent resistance will be,

The potential source should constitute the same potential as in the base terminal. So, it is basically going to be the voltage drop across 20k resistance.

So, it will be,

Also, I_E = I_B + I_c and I_c = βI_B

From loop1,

Now, from loop2,

Putting the values of R_E we can find R_C.