MathDB

Let

p, q

and

r

be three concurrent lines in the plane such that the angle between any two of them is

60^o

. Let

a

b

and

c

be real numbers such that

0 < a \le b \le c

.
(a) Prove that the set of points whose distances from

p, q

and

r

are respectively less than

a, b

and

c

consists of the interior of a hexagon if and only if

a + b > c

.
(b) Determine the length of the perimeter of this hexagon when

a + b > c

3