MathDB

4

Part of 1969 Dutch Mathematical Olympiad

Problems(1)

triangle with minimal perimeter , 2 vertices on legs of an angle

Source: Netherlands - Dutch NMO 1969 p4

2/1/2023
An angle <45o< 45^o is given in the plane of the drawing. Furthermore, the projection P1P_1 of a point PP lying above the plane of the drawing and the distance from PP to P1P_1 are given. P1P_1 lies within the given angle. On the legs of the given angle, construct points AA and BB, respectively, such that the triangle PABPAB has a minimal perimeter.
geometryperimetergeometric inequalityconstruction