Question 148
Given $n$-gon $P$ inscribed in the unit circle.
a) Show that there exist a point lie on the unit circle such that multiplication of distances between above point and for every vertices of $P$ greater than or equal to $2$.
b) If there is not exist a point in the unit circle such that multiplication of distances between above point and for every vertices of $P$ greater than $2$ then prove that $P$ is regular.
(proposed by N. Byambajav)
a) Show that there exist a point lie on the unit circle such that multiplication of distances between above point and for every vertices of $P$ greater than or equal to $2$.
b) If there is not exist a point in the unit circle such that multiplication of distances between above point and for every vertices of $P$ greater than $2$ then prove that $P$ is regular.
(proposed by N. Byambajav)