MathSaiyan wrote: Let $ABC$ be a triangle with circumcircle $\Omega$, and let $P$ be a point on the arc $BC$ of $\Omega$ not containing $A$. Let $\omega_B$ and $\omega_C$ be circles respectively passing through $B$ and $C$ and such that both of them are tangent to line $AP$ at point $P$. Let $R$, $R_B$, $R_C$ be the radii of $\Omega$, $\omega_B$, and $\omega_C$, respectively. Prove that if $h$ is the distance from $A$ to line $BC$, then \[ \frac{R_B+R_C}{R} \le \frac{BC}{h}. \] Let $\measuredangle BAP=\alpha_1$ and $\measuredangle CAP=\alpha_2$. Thus, $\alpha_1+\alpha_2=\alpha$ and we need to prove that: $$\sin\alpha_1\sin\gamma+\sin\alpha_2\sin\beta\leq\sin\alpha,$$which is trivial.