MathDB

Let

A,B

be different points on a parabola. Prove that we can find

P_1,P_2,\dots,P_{n}

between

A,B

on the parabola such that area of the convex polygon

AP_1P_2\dots P_nB

is maximum. In this case prove that the ratio of

S(AP_1P_2\dots P_nB)

to the sector between

A

and

B

doesn't depend on

A

and

B

, and only depends on

n

Problem Statement