Challenge 397: Smallest Sum of Squares
Calculate the smallest value of the sum of the squares of these distances!
PQRS is a quadrilateral composed of an equilateral triangle (PQS) with side length 2 units, and an isosceles triangle (QRS) with a right angle at R, and sides RQ = RS. R and P are on opposite sides of the line QS.
X is a point inside PQRS.
The quantity T is given by
T = XP2 + XQ2 +XR2 + XS2
What is the smallest possible value of T, and where is X when this smallest value is attained?