MathNet 2025-part-02 — 186 problems (EN–VI) Question 145

Point $P$ is inside triangle $\triangle ABC$ such that $\angle ABP = \angle ACP$. Given that $AB = 6$, $AC = 8$, $BC = 7$, and $\frac{BP}{PC} = \frac{1}{2}$, compute $\frac{|BPC|}{|ABC|}$.

(Here, $[XYZ]$ denotes the area of $\triangle XYZ$.)