Subcontests
(6)2/(1/d_a + 1/d_b + 1/dc) < r < (d_a + d_b + d_c)/2
P is a point inside the triangle ABC is a triangle. The distance of P from the lines BC,CA,AB is da,db,dc respectively. If r is the inradius, show that da1+db1+dc12<r<2da+db+dc p(cos t, sin t) = 0, p(x,y) = (x^2 + y^2 - 1) q(x,y), polynomials
p(x,y) is a polynomial such that p(cost,sint)=0 for all real t.
Show that there is a polynomial q(x,y) such that p(x,y)=(x2+y2−1)q(x,y). square can be covered with rectangles R_i with sides // to square sides
Given a square side 1 and 2n positive reals a1,b1,...,an,bn each ≤1 and satisfying ∑aibi≥100. Show that the square can be covered with rectangles Ri with sides length (ai,bi) parallel to the square sides. max k nos in set {n+1, n+2, ... , n+16} which are coprime with n(n+17)
Find the largest k such that for every positive integer n we can find at least k numbers in the set {n+1,n+2,...,n+16} which are coprime with n(n+17).