HYACINTHOS 21096

 

 

Dear Randy,

The conversion of the coordinates of some point wrt a Triangle-1 to the coordinates wrt a Triangle-2 can be done using the theory of Perspective Fields.
See Perspective Fields Part II, for example page 40 at:
http://www.chrisvantienhoven.nl/mathematics/perspective-fields.html

I calculated these results:
X(11) = X(110) wrt Incentral Triangle
X(3024) = X(930) wrt Incentral Triangle
X(115) doesn't lie on the incircle,
and is no existing ETC-point wrt Incentral Triangle

I checked some other points on the incircle:
X(1317) = X(74) wrt Incentral Triangle
X(1355) = no existing ETC-point wrt Incentral Triangle
X(1356) = no existing ETC-point wrt Incentral Triangle
X(1357) = X(107) wrt Incentral Triangle
X(1358) = X(112) wrt Incentral Triangle
X(1359) = X(1299) wrt Incentral Triangle
X(1360) = X(3563) wrt Incentral Triangle
X(1361) = X(1300) wrt Incentral Triangle
X(1362) = X(98) wrt Incentral Triangle
X(1363) = no existing ETC-point wrt Incentral Triangle
X(1364) = X(925) wrt Incentral Triangle
X(1365) = X(933) wrt Incentral Triangle
X(1366) = no existing ETC-point wrt Incentral Triangle
X(1367) = no existing ETC-point wrt Incentral Triangle


It also looks like the problem of converting a point in a Complete Quadrangle from coordinates expressed wrt the Diagonal Triangle to coordinates wrt a Component Triangle and vice versa.
See:
http://www.chrisvantienhoven.nl/quadrangle-objects/15-mathematics/quadrangle-objects/artikelen-qa/36-qa-6.html
and:
http://www.chrisvantienhoven.nl/quadrangle-objects/15-mathematics/quadrangle-objects/artikelen-qa/37-qa-7.html

It also looks like the problem of converting a point in a Complete Quadrilateral from coordinates expressed wrt the Diagonal Triangle to coordinates wrt a Component Triangle and vice versa.
See:
http://chrisvantienhoven.nl/quadrilateral-objects/17-mathematics/encyclopedia-of-quadri-figures/quadrilateral-objects/artikelen-ql/101-ql-6.html
and:
http://chrisvantienhoven.nl/quadrilateral-objects/17-mathematics/encyclopedia-of-quadri-figures/quadrilateral-objects/artikelen-ql/106-ql-7.html


If you want to know the barycentric coordinates wrt the Incentral triangle, or other points on the Incircle to be converted, just let me know.

Best regards,

Chris van Tienhoven

 

--- In Hyacinthos@yahoogroups.com, "rhutson2" <rhutson2@...> wrote:
>
> Dear Hyacinthists,
>
> What is the point P for which P of the incentral triangle = X(11)?
>
> What is the point Q for which Q of the incentral triangle = X(115)?
>
> What is the point R for which R of the incentral triangle = X(3024)?
>
> Since X(11), X(115) and X(3024) lie on the incentral circle, P, Q and R lie on the circumcircle of ABC.
>
> I have checked the usual suspects, X(74), X(98)-X(112), X(476), and their antipodes, but no luck.
>
> Thanks in advance,
> Randy Hutson
>