MathDB

2

Part of 1995 Rioplatense Mathematical Olympiad, Level 3

Problems(1)

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

Source: Rioplatense 1995 L3 p2

5/26/2019
In a circle of center OO and radius rr, a triangle ABCABC of orthocenter HH is inscribed. It is considered a triangle A′B′C′A'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 A′B′C′A'B'C' is maximum.
geometryarea of a triangleorthocenterinradius