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Challenge 374: Circle Challenge

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 Vto 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