area of triangle, medians
Source: 2021 Dürer Math Competition Finals Day2 E10 https://artofproblemsolving.com/community/c2749870_
January 9, 2022
geometryareas
Problem Statement
A triangle is given. Its side a is of length cm, and its area is cm. It is also known that one of the angles lying on side a is twice as large as the other one. We cut the triangle into two parts at the median belonging to side a. Then we move the so-obtained two parts towards each other, such that the two segments of side a remain on the same line (i.e., the line initially occupied by side a). We move the two parts towards each other until we first reach a moment when the common part of the two segments is of length cm. What is the area of the so-obtained shape in cm? The so-obtained shape is the union of the two parts, which is a heptagon.
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