Points $A$ and $C$ with position vectors $\bf u$ and $\bf v$ lie on the circle centre $\bf 0$ and radius $r$. Tangents to the circle at $A$ and $C$ meet at the point $B$ with position vector $\bf w$.
How can I show, using the perpendicular property of tangents, that $\bf w \bullet u$ $= r^2$ and $\bf w \bullet v$ $= r^2$ and that $\bf \vec{OB}$ is perpendicular to $\bf \vec{AC}$?