Proving Ceva's Theorem with Triangle PQR

[tomz]

I have tried but still cannot get it. Simple geometry question.

Tangents to the inscribed circle of triangle PQR are parallel to [QR], [RP] and [PQ]
respectively and they touch the circle at A, B and C.
Prove that [PA], [QB] and [RC] are concurrent

relevant formula:

Ceva's theorem (Any three concurrent lines drawn from the vertices of a triangle divide the sides (produced if necessary) so that the product of their respective ratios is unity/

Thank you in advance!

I have tried on geometry sketch pad. It did works...

 

[coolul007]

some thoughts: The parallel lines form a triangle congruent to the first rotated 180 degrees. The tangents of both triangles have a corresponding point 180 degrees apart on the circle.