MathDB

4

Part of 1961 Czech and Slovak Olympiad III A

Problems(1)

Extrema of area of triangle

Source: Czech and Slovak Olympiad 1961, National Round, Problem 4

6/16/2024
Consider a unit square ABCDABCD and a (variable) equilateral triangle XYZXYZ such that X,ZX, Z lie on rays AB,DC,AB, DC, respectively, and YY lies on segment ADAD. Compute the area of triangle XYZXYZ in terms of x=AXx=AX and determine its maximum and minimum.
geometryEquilateralTrianglecomputationtriangle areamaxmin