In triangle ABC, AB=425, BC=450, CA=510. Moreover, P is an interior point chosen so that segments DE, FG, HI are each of length d, contain P,and are parallel to sides AB, BC, CA, respectively, where D and G lie on segment CA; E and H lie on segment BC; F and I line on segment AB. Compute d.

(第四届AIME1986 第9题)