ADGEOM 1427 * ADGEOM 1430

 

#1427

Dear Members!

Let ABC be a triangle. Point P is on it's circumcircle. Tangents at P to incircle of ABC intersect incircle and circumcircle in four points - let X_{P} be the intersection of it's diagonals. Then X_{P} (where P lies on circumcircle) lies on circle which contains Gergonne point of ABC and it's center in 6,9,13 is 1.084338...

Best regards, 

Dominik Burek 

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#1430

Dear Dominik, nice circle indeed!

I find that your circle has the point X1159 as center, and radius r (R - 2 r)/(4 R + r).

Best regards,

Francisco Javier.