Question 75
Let $ABC$ be a triangle with a right angle at $A$, such that $A'$ is the midpoint of the hypotenuse, $M$ is the midpoint of the altitude $AD$, $D \in BC$, and $\{P\} = BM \cap AA'$.
Denoting $\alpha = m(\widehat{PCB})$, prove that
$$
\operatorname{tg} \alpha = \sin C \cdot \cos C
$$
Denoting $\alpha = m(\widehat{PCB})$, prove that
$$
\operatorname{tg} \alpha = \sin C \cdot \cos C
$$