MathDB

3

Part of 2006 Austrian-Polish Competition

Problems(1)

Is the tetrahedron regular?

Source: Austrian-Polish 2006 Question3

8/21/2006
ABCDABCD is a tetrahedron. Let KK be the center of the incircle of CBDCBD. Let MM be the center of the incircle of ABDABD. Let LL be the gravycenter of DACDAC. Let NN be the gravycenter of BACBAC. Suppose AKAK, BLBL, CMCM, DNDN have one common point. Is ABCDABCD necessarily regular?
geometry3D geometrytetrahedrongeometry proposed