SMO senior test (2nd round)

Ahhhh... i suck at geometry..
Of the five questions, two were geom and both of which i was unable to solve... argh.. somone pro at geom pls teach me geom..

ok i hav decided to post the questions and maybe at a later date i will post the answers.. my answer for q4 will be a bit messy so someone else please help me refine it..

here are the questions (the phrasing is really bad!!)

1)a and d are numbers such that a, a+d, a+2d are all prime numbers
larger than 3 show that d is a multiple of 6.

2)ABCD is a cyclic quadrilateral, let the bisectors of A and B meet
at E. Draw a line parallel to CD through E. Let the line intersect AD
at L and BC at M show that ML=AL+BM.

3)Two circles are tangent to each other internally at T. Let AB be
tangent to the smaller circle at P where A and B lie on the bigger
circle. Show that AP bisects angle ATB.

4)You are given several congruent equilateral triangles. Can there
exist a convex hexagon with all internal angles equal to 120 deg
which is formed with 19 of the pieces. 20 pieces? note: the smallest
are of the form 6,10,13.

5)(i)determine if 526315789473684210 is "persistant".
where a persistant number is defined as a number that contains all
digits from 0 to 9 when multiplied by any integer.
(ii) are there any "persistant" numbers smaller than the given number?