I got 3 questions to solve here.

1) if: x^2 + x + 1 = 0 then calculate: x^3333 + x^333+ x^33 + x^3 + 3 = ?

2) a^2 + b^2 + c^2 + d^2 = ab + bc + cd + da

Prove: a=b=c=d

3) You are given a circles diameter and a point that lies above the diameter. without using a protractor how would one find the EXACT perpendicular line (EXACTLY 90 degrees) from the point to the diameter.

Thanksies :)