Question 133
They are $ABC$ a sharp-angled triangle with the $\angle BAC=45^{\circ}$ property. They $D$ the perpendicular base point from $C$ on $AB$. They are $P$ an internal point of the line segment $CD$. Prove that the lines $AP$ and $BC$ are perpendicular to each other and only then as $|AP|=|BC|$.