line construction such that intersection with angle has given area
Source: 2004 VMEO I p3 Vietnamese Mathematics e - Olympiad https://artofproblemsolving.com/community/c2461015_vmeo__vietnam_mathematical
September 26, 2021
geometryconstructionareas
Problem Statement
In the plane, given an angle .
a) Given a triangle of area , describe how to construct a triangle of given area and altitude . Using this, describe how to construct parallelogram A with two sides lying on and , the area and the distance between the two opposite sides equal to d given.
b) From an arbitrary point on the line , construct a line that intersects the lines B, , at , and respectively so that the area of triangle is equal to the area of parallelogram .
c) Apply the above two sentences: Given any point in the plane. From , construct a line that intersects two rays and at and respectively so that the area of triangle is equal to the area of any given triangle.