junior area chasing, 3 equal segments, 2 equilaterals (2023 May Olympiad L1 p3)
Source:
March 24, 2024
geometryareas
Problem Statement
On a straight line there are four points, , , and in that order, such that . A point is chosen outside the straight line so that when drawing the segments and , an equilateral triangle is formed . Segments and are drawn, and a point is chosen so that when drawing the segments and , an equilateral triangle is formed outside the triangle . Finally, the lines and are drawn , which intersect at the point . If the area of triangle is , calculate the area of triangle .