Given a regular triangle $ABC$, whose area is $1$, and the point $P$ on its circumscribed circle. Lines $AP, BP, CP$ intersect, respectively, lines $BC, CA, AB$ at points $A', B', C'$. Find the area of the triangle $A'B'C'$.
Problem
Source: 2014 Oral Moscow Geometry Olympiad grades 10-11 p5
Tags: geometry, circumcircle, area of a triangle, area, Equilateral, Equilateral Triangle
