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Sum Reciprocal Lengths (Posted on 2007-11-17) Difficulty: 2 of 5
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.

See The Solution Submitted by K Sengupta    
Rating: 2.5000 (2 votes)

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Solution Solution | Comment 5 of 6 |

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

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