Each of the sides PQ, QR, RS, ST, TU, UV and VP of a regular heptagon
PQRSTUV have length 2. The respective lengths of two of the diagonals PR and PS of the heptagon are denoted by X and Y.
Determine 1/X + 1/Y.
Consider the quadrilateral defined by points P, Q, R, and T. The sides are PQ=2, QR=2, RT=X, TP=Y and the diagonals are PR=X and QT=Y.
Then apply Ptolemy's Theorem
2*X + 2*Y = X*Y
1/Y + 1/X = 1/2