Question 6
Let $ABC$ be a triangle. Find all $P$ on segment $BC$ with the following property. If $X,Y$ are the intersections of line $PA$ with the common external tangent lines of the circumcircles of $PAB,PAC$, then
$$\left(\frac{PA}{XY}\right)^2+\frac{PB\cdot PC}{AB\cdot AC}=1.$$
Proposed by Titu Andreescu, Cosmin Pohoata (as credited in the supplied compilation).
$$\left(\frac{PA}{XY}\right)^2+\frac{PB\cdot PC}{AB\cdot AC}=1.$$
Proposed by Titu Andreescu, Cosmin Pohoata (as credited in the supplied compilation).