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MathNet 2026 — Part 07 Question 167

Math Olympiad Vault · MathNet 2026 — Part 07

Question 167

Point $P$ on side $BC$ of triangle $ABC$ satisfies
$$
|BP| : |PC| = 2 : 1
$$
Prove that the line $AP$ bisects the median of triangle $ABC$ drawn from vertex $C$.