Four contact-points of a side and incircle, excircles of a triangle ?

[lvl107]

Hello Everyone.
From the following :
Given :
Let four contact-points of a side and incircle, excircles of a triangle are the pink point, green point, red point and blue point.
Prove :
Distance from the pink point to the red point = distance from the green point to the blue point . ( see figure )

Thanks in advance for your time and help.
Best Regards.
Loi.

[JP_10582902]

Necesito las dimensions del triangulo o el radio de circunferencia inscrita. Me avisas y te ayudare.