MathDB

1

Part of 1973 Dutch Mathematical Olympiad

Problems(1)

inscribed trriangle with min perimeter in a triangle with angle 60^o

Source: Netherlands - Dutch NMO 1973 p1

1/27/2023
Given is a triangle ABCABC, ∠C=60o\angle C = 60^o, RR the midpoint of side ABAB. There exist a point PP on the line BCBC and a point QQ on the line ACAC such that the perimeter of the triangle PQRPQR is minimal. a) Prove that and also indicate how the points PP and QQ can be constructed. b) If AB=cAB = c, AC=bAC = b, BC=aBC = a, then prove that the perimeter of the triangle PQRPQR equals 123c2+6ab\frac12\sqrt{3c^2+6ab} .
geometryperimetergeometric inequality