Let A (6,8), B (10 cos α,-10 sin α) and C (-10 sin α, 10 cos α), be the vertices of a triangle. If L(a, 9) and G(h, k) be its orthocenter and…

Let $\displaystyle \mathrm{A}(6,8), \mathrm{B}(10 \cos \alpha,-10 \sin \alpha)$ and $\displaystyle \mathrm{C}(-10 \sin \alpha, 10 \cos \alpha)$, be the vertices of a triangle. If $\displaystyle L(a, 9)$ and $\displaystyle G(h, k)$ be its orthocenter and centroid respectively, then $\displaystyle (5 a-3 h+6 k+100 \sin 2 \alpha)$ is equal to $\displaystyle \_\_\_\_$.