Here is another complex geometry problem- Q.In a regular planar n-gon , 7 diagonals are concurrent at a point Q.Find least possible value of n.It is given that Q is not the center of the polygon.
On Jan 12, 6:35 pm, Sujeet Kumar <sujeetkumar...@gmail.com> wrote:
> Here is another complex geometry problem- > Q.In a regular planar n-gon , 7 diagonals are concurrent at a point Q.Find least possible value of n.It is given that Q is not the center of the polygon.
> **Be wise, generalise.**
By a diagonal is meant a straight line joining non-adjacent vertices? n=10.
One vertex Q, chosen as point of concurrency, is joined to remaining 7 non-adjacent vertices of a regular decagon ( n = 10) forming 10 -3 = 7 diagonals.
> On Jan 12, 6:35 pm, Sujeet Kumar > <sujeetkumar...@gmail.com> wrote: > > Here is another complex geometry problem- > > Q.In a regular planar n-gon , 7 diagonals are > concurrent at a point Q.Find least possible value of > n.It is given that Q is not the center of the > polygon.
> > **Be wise, generalise.**
> By a diagonal is meant a straight line joining > non-adjacent vertices? > n=10.
> One vertex Q, chosen as point of concurrency, is > joined to remaining > 7 non-adjacent vertices of a regular decagon ( n = > 10) forming 10 -3 = > 7 diagonals.
> Narasimham
I am not getting your solution.Send a diagram.Any n which is multiple of 30 will have this property.So least value will be 30. Regards from Sujeet
> > On Jan 12, 6:35 pm, Sujeet Kumar > > <sujeetkumar...@gmail.com> wrote: > > > Here is another complex geometry problem- > > > Q.In a regular planar n-gon , 7 diagonals are > > concurrent at a point Q.Find least possible value of > > n.It is given that Q is not the center of the > > polygon.
> > > **Be wise, generalise.**
> > By a diagonal is meant a straight line joining > > non-adjacent vertices? > > n=10.
> > One vertex Q, chosen as point of concurrency, is > > joined to remaining > > 7 non-adjacent vertices of a regular decagon ( n = > > 10) forming 10 -3 = > > 7 diagonals.
> > Narasimham
> I am not getting your solution.Send a diagram.Any n which is multiple of 30 will have this property.So least value > will be 30. > Regards from Sujeet
May be a trivial or extreme solution. If a JavaSketchPad drawn with all 5 radial lines as diagonals concurring at center of n =10 decagon and then if center is dragged to any vertex, a diagram of 7 diagonals would form as in:
> On Jan 26, 7:32 pm, Sujeet Kumar > <sujeetkumar...@gmail.com> wrote: > > > On Jan 12, 6:35 pm, Sujeet Kumar > > > <sujeetkumar...@gmail.com> wrote: > > > > Here is another complex geometry problem- > > > > Q.In a regular planar n-gon , 7 diagonals are > > > concurrent at a point Q.Find least possible value > of > > > n.It is given that Q is not the center of the > > > polygon.
> > > > **Be wise, generalise.**
> > > By a diagonal is meant a straight line joining > > > non-adjacent vertices? > > > n=10.
> > > One vertex Q, chosen as point of concurrency, is > > > joined to remaining > > > 7 non-adjacent vertices of a regular decagon ( n > = > > > 10) forming 10 -3 = > > > 7 diagonals.
> > > Narasimham
> > I am not getting your solution.Send a diagram.Any n > which is multiple of 30 will have this property.So > least value > > will be 30. > > Regards from > Sujeet
> May be a trivial or extreme solution. If a > JavaSketchPad drawn with > all 5 radial lines as diagonals concurring at center > of n =10 decagon > and then if center is dragged to any vertex, a > diagram of 7 diagonals > would form as in:
