# Inequality on simplex with circumscribed sphere

I'm looking for a proof for this problem on simplex which I think it is true

Question. Let $\mathcal{A}=A_0A_1...A_n$ be a simplex in $\Bbb E^n$. $(S)$ is circumscribed sphere of $\mathcal{A}$ with center $O$ and radius $R$. $P$ is a point inside $\mathcal{A}$. Lines $PA_i$ meets $(S)$ again at $B_i$, $i=\overline{0,n}$. Let $r_A$ and $r_B$ be the radius of inscribed sphere of the simplex $\mathcal{A}=A_0A_1...A_n$ and $\mathcal{B}=B_0B_1...B_n$. Prove that $$R^2\ge n^2r_A\cdot r_B+OP^2.$$

• It seems you should add some more context to your question, otherwise it will get closed. – András Bátkai Jul 10 '18 at 17:27
• Thank Prof. András Bátkai, I apologize if this question has not reached the research level. I will delete it if you are not interested in this. – Tran Quang Hung Jul 11 '18 at 5:26