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.

Look at cyclic quadrilateral PRST,

  |PS||RT| = |PR||ST| + |PT||RS|

           or

  XY = 2X + 2Y = 2(X + Y) 

Therefore,

   1     1     X + Y     1
  --- + --- = ------- = ---
   X     Y      XY       2

Edited on November 18, 2007, 2:32 am

Posted by Bractals on 2007-11-18 02:23:37