MathDB
triangle with max area, sides related to segments of a given triangle

Source: Rioplatense 1995 L3 p2

May 26, 2019
geometryarea of a triangleorthocenterinradius

Problem Statement

In a circle of center OO and radius rr, a triangle ABCABC of orthocenter HH is inscribed. It is considered a triangle ABCA'B'C' whose sides have by length the measurements of the segments AB,CHAB, CH and 2r2r. Determine the triangle ABCABC so that the area of the triangle ABCA'B'C' is maximum.