MathDB

\triangle ABC

has semiperimeter

s

and area

F

. A square

P QRS

with side length

x

is inscribed in

ABC

with

P

and

Q

BC

R

AC

, and

S

AB

. Similarly,

y

and

z

are the sides of squares two vertices of which lie on

AC

and

AB

, respectively. Prove that

\frac 1x +\frac 1y + \frac 1z \le \frac{s(2+\sqrt3)}{2F}

Problem Statement