SHARYGIN 2013 Problem 11

a) Let $ABCD$ be a convex quadrilateral and $r_1 \le r_2 \le r_3 \le r_4$ be the radii of the incircles of triangles $ABC, BCD, CDA, DAB$ . Can the inequality $r_4 > 2r_3$ hold?

b) The diagonals of a convex quadrilateral $ABCD$ meet in point $E$ . Let $r_1 \le r_2 \le r_3 \le r_4$ be the radii of the incircles of triangles $ABE, BCE, CDE, DAE$ . Can the inequality $r_2 > 2r_1$ hold?