The green shape is the border of the cone [math]\{(x_1,x_2,t)\mid \|(x_1,x_2)\|_1\leq t\}[/math]. The blue plane is [math]\{(c_1 - y a_1, c_2 - y a_2, t)\mid y,t\in\mathbb{R}\}[/math]. The red point is [math](c_1 - y a_1, c_2 - y a_2, t)[/math] at the optimal of [math]\min_{y,t} \quad t [/math] [math]\text{s.t.}\quad \|\mathbf{c}-y\mathbf{a}\|_1 \leq t[/math].