MathDB

Given isosceles tetrahedron

PABC

(faces are equal triangles). Let

A_0

B_0

and

C_0

be the touchpoints of the circle inscribed in the triangle

ABC

with sides

BC

AC

and

AB

respectively,

A_1

B_1

and

C_1

are the touchpoints of the excircles of triangles

PCA

PAB

and

PBC

with extensions of sides

PA

PB

and

PC

, respectively (beyond points

A

B

C

). Prove that the lines

A_0A_1

B_0B_1

and

C_0C_1

intersect at one point.

Problem Statement