p13 Let ABCD be a square. Points E and F lie outside of ABCD such that ABE and CBF are equilateral triangles. If G is the centroid of triangle DEF, then find ∠AGC, in degrees.
p14 The silent reading s(n) of a positive integer n is the number obtained by dropping the zeros not at the end of the number. For example, s(1070030)=1730. Find the largest n<10000 such that s(n) divides n and n=s(n).
p15 Let ABCDEFGH be a regular octagon with side length 12. There exists a region R inside the octagon such that for each point X in R, exactly three of the rays AX, BX, CX, DX, GX, and HX intersect segment EF. If the area of region R can be expressed as a−bc for positive integers a,b,c with c squarefree, find a+b+c. geometrynumber theoryYale