A square S has vertices V₁, V₂, V₃ and V₄ which lie on the circumference of a circle C with radius 1.

T is a straight line which is tangent to circle C.

The shortest distances from V₁, V₂, V₃ and V₄ to T are d₁, d₂, d₃, and d₄ respectively.

Show that the value of all of the following expressions remain constant, regardless of how T is positioned in relation to S.

(i) d₁ + d₂ +d₃ + d₄

(ii) d₁² + d₂² +d₃² + d₄²

(ii) d₁³ + d₂³ +d₃³ + d₄³