Question 16
A circle $\mathcal C$ has equation $(x-10)^2+(y-10\sqrt3)^2=39$. Let $a$ be largest real number such that the line $\mathcal L$ tangent to $\mathcal C$ at the point $(a,b)$ passes through the origin. Given that
$$\frac ba=\alpha\sqrt3+\beta\sqrt{39}$$
find the value of $\left\lceil\left|\frac\alpha\beta\right|\right\rceil$, where $\alpha,\beta$ are rational numbers in their simplest form.
$$\frac ba=\alpha\sqrt3+\beta\sqrt{39}$$
find the value of $\left\lceil\left|\frac\alpha\beta\right|\right\rceil$, where $\alpha,\beta$ are rational numbers in their simplest form.