MathDB

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

Source: Netherlands - Dutch NMO 1973 p1

January 27, 2023

geometryperimetergeometric inequality

Problem Statement

Given is a triangle

ABC

\angle C = 60^o

R

the midpoint of side

AB

. There exist a point

P

on the line

BC

and a point

Q

on the line

AC

such that the perimeter of the triangle

PQR

is minimal. a) Prove that and also indicate how the points

P

and

Q

can be constructed. b) If

AB = c

AC = b

BC = a

, then prove that the perimeter of the triangle

PQR

equals

\frac12\sqrt{3c^2+6ab}