Interactive step-by-step animation using GeoGebra. Post your solution in the comment box below. Level: Mathematics Education, High School, Honors Geometry, College.
Define points A,B,C,D,E,F as shown on the sketch Perform geometric inversion with center at P and circle power k = PP34. PA=PP24. PD=PP14. PE=PP12. PC= PP23. PF=PP13. PB In this inversion ,Green circles C1 , C2, C3 and C4 will become Lines BCE, DCF, ABF, and ADE. And red circles C123, C124, C234 and C134 will become Circumcircles of triangles FBC, CDE, ADF and ABE. Per the result of problem 547 ( see link below) https://gogeometry.blogspot.com/2010/12/problem-547-triangle-transversal.html These 4 circles will meet at a point G So 4 red circles will meet at a point M , image of G in this geometric inversion Such that PM.PG= k
https://photos.app.goo.gl/oeaR3NCro86whAueA
ReplyDeleteDefine points A,B,C,D,E,F as shown on the sketch
Perform geometric inversion with center at P and circle power k
= PP34. PA=PP24. PD=PP14. PE=PP12. PC= PP23. PF=PP13. PB
In this inversion ,Green circles C1 , C2, C3 and C4 will become
Lines BCE, DCF, ABF, and ADE.
And red circles C123, C124, C234 and C134 will become
Circumcircles of triangles FBC, CDE, ADF and ABE.
Per the result of problem 547 ( see link below)
https://gogeometry.blogspot.com/2010/12/problem-547-triangle-transversal.html
These 4 circles will meet at a point G
So 4 red circles will meet at a point M , image of G in this geometric inversion
Such that PM.PG= k