MathNet 2020 — Math Olympiad Vault — Part 06 Question 49

Let $M$ be the middle point of the side $AC$ of triangle $ABC$. Inside $\triangle BMC$, there is such point $P$ that $\angle BMP = 90^\circ$, $\angle ABC + \angle APC = 180^\circ$. Prove that $\angle PBM + \angle CBM = \angle PCA$.

(Anton Tryhub)

Editorial note: the source solution refers to Figure 26, but the supplied record contains no corresponding image. The point construction is specified in the text.