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 Cyclic Hexagon And Ratio (Posted on 2007-12-08)
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.)
 re: More Thoughts | Comment 4 of 6 |
(In reply to More Thoughts by Brian Smith)

Without a Geometer's Sketchpad it is difficult to find where the diagonals PS, QT and RU might meet at point V and where PR = 3*RT, and I suspect it might be easier to algebraically and trigonometrically solve this.  Nonetheless, using Paint as my "Geometer's Sketchpad" I can give what I believe might be an approximate ratio -- 8:1.  Unfortunately I can not yet prove this nor be certain how close to accurate my guess is.

Edited on December 11, 2007, 3:53 am
 Posted by Dej Mar on 2007-12-10 06:43:44

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