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Cyclic Hexagon And Ratio (Posted on 2007-12-08) Difficulty: 3 of 5
The six sides of a cyclic hexagon PQRSTU are PQ, QR, RS, ST, TU and UP. It is known that PQ= RS= TU and the diagonals PS, QT and RU meet at the point V. The lines PS and RT intersect at the point W.

Determine the ratio RW/WT, given that PR = 3*RT.

                         .  . .  .  . .  .
                    .                         .
                 .                               .
              .                                     .
            .                                         .
          .                                             .
        .Q                                              R .
       .                                                   .
      .                                                     .
     .                                                       .
    .                                                         .

   .                                                           .
   .                                                           .
   .                                                    V     WS
   P                                                           T
   .                                                           .

    .                                                         .
     .                                                       .
      .                                                     .
       .                                                   .
        .                                                 .
          .                                             .
            .                                         .U
              .                                     .
                 .                               .
                    .                         .
                         .  . .  .  . .  .


Unfortunately the reader must visualise the lineal connections.

No Solution Yet Submitted by K Sengupta    
Rating: 4.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
3 times isosceles | Comment 5 of 6 |
There is a point "O", the centre of the circle on whose circumference the hexagonal points lie. 

Given that  "PQ= RS= TU" we also might need to know that we have 3 isosceles triangles with apices at O.  How might that influence our thoughts?

Oh, and Charlie's graphic here suggests (note with due reservations) that P,V,W & S could be collinear.

Edited on December 10, 2007, 9:13 am
  Posted by brianjn on 2007-12-10 08:50:07

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