MathDB

As shown in figure , the inscribed circle of

ABC

is intersects

BC

CA

AB

at points

D

E

F

, repectively, and

P

is a point inside the inscribed circle. The line segments

PA

PB

and

PC

intersect respectively the inscribed circle at points

X

Y

and

Z

. Prove that the three lines

XD

YE

and

ZF

have a common point. https://cdn.artofproblemsolving.com/attachments/e/9/bbfb0394b9db7aa5fb1e9a869134f0bca372c1.png

Problem Statement