Given a triangle $ABC$, a line in its plane is called a cool if it divides the triangle into two parts with equal areas and perimeters. a) Does there exist a triangle $ABC$ with at least seven cool lines? b) Prove that all cool lines intersect at a point $X$. If $\angle AXB = 126^\circ$, prove that $(8\sin^2 \angle ACB - 5)^2$ is an integer.