MathDB

16.3

Part of Geometry Mathley 2011-12

Problems(1)

Geometry Mathley 16.3 concurrent

Source:

6/14/2020
The incircle (I)(I) of a triangle ABCABC touches BC,CA,ABBC,CA,AB at D,E,FD,E, F. Let ID,IE,IFID, IE, IF intersect EF,FD,DEEF, FD,DE at X,Y,ZX,Y,Z, respectively. The lines ℓa,ℓb,ℓc\ell_a, \ell_b, \ell_c through A,B,CA,B,C respectively and are perpendicular to YZ,ZX,XYYZ,ZX,XY . Prove that ℓa,ℓb,ℓc\ell_a, \ell_b, \ell_c are concurrent at a point that is on the line segment joining II and the centroid of triangle ABCABC .
Nguyễn Minh Hà
geometryconcurrentincircle