Dj Rectangle

Geometry question – help?
In rectangle ABCD, diagonal AC and BD intersect at H. E is in the CD, F is between H and C, G lies between H and D, and J is between A and H such that EF is perpendicular to AC, EG is perpendicular to BD, and DJ is perpendicular to AC. If BD = 20, and HJ = 7, then find radical in simplest form, the value of EG + EF. Please help? I am very confused!
General rule on issues like that – draw the image with a large number of right triangles, perhaps even dropping additional angles as necessary, and use the Pythagorean Theorem lot.
DJ RECTANGLE – 1993 DMC USA FINALS CHAMP
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