>>13243343QT = 2x
QR = x+k
QP = ST = x
PR+RS = y
PR= x^2+(x+k)^2
RS= x^2+(x-k)^2
y=2(x^2)+(x-k)^2+(x+k)^2
y=2x^2+2x^2+2k^2-2xk+2xk
y=4x^2+2k^2
dy/dk=4k
when k =0, dy/dk is zero
since d(dy/dk)/dk is 4, which is positive, when k=0, y is at a minimum.
Shortest distance is therefore when k=0 or when QR=QT
Since QP=ST, we can use proposition 4 from Euclid's elements to assert that all angles are the same
