Question 77
Let $ABCD$ be a square. Consider a variable point $P$ inside the square for which $\angle BAP \geq 60^{\circ}$. Let $Q$ be the intersection of the line $AD$ and the perpendicular to $BP$ in $P$. Let $R$ be the intersection of the line $BQ$ and the perpendicular to $BP$ from $C$.
a. Prove that $|BP| \geq |BR|$.
b. For which point(s) $P$ does the inequality in (a) become an equality?
a. Prove that $|BP| \geq |BR|$.
b. For which point(s) $P$ does the inequality in (a) become an equality?