MathDB

Let

S

be any point on the circumscribed circle of

PQR.

Then the feet of the perpendiculars from S to the three sides of the triangle lie on the same straight line. Denote this line by

l(S, PQR).

Suppose that the hexagon

ABCDEF

is inscribed in a circle. Show that the four lines

l(A,BDF),

l(B,ACE),

l(D,ABF),

and

l(E,ABC)

intersect at one point if and only if

CDEF

is a rectangle.

Problem Statement