Question 42
A regular pentagon is inscribed in a circle of radius $r$. $P$ is any point inside the pentagon. Perpendiculars are dropped from $P$ to the sides, or the sides produced, of the pentagon.
a) Prove that the sum of the lengths of these perpendiculars is constant.
b) Express this constant in terms of the radius $r$.
a) Prove that the sum of the lengths of these perpendiculars is constant.
b) Express this constant in terms of the radius $r$.