(a) ABC is a triangle in which $$AB=24$$, $$BC=10$$ and $$CA=26$$. P is a point inside the triangle. Perpendiculars are drawn to BC, AB and AC. Lengths of these perpendiculars respectively are x, y and z. Find the numerical value of $$5x+12y+13z$$. 

(b) If $$x^2(y+z)=a^2$$, $$y^2(z+x)=b^2$$, $$z^2(x+y)=c^2$$, $$xyz=abc$$, prove that $$a^2+b^2+c^2+2abc=1$$.