MathDB

A triangle

ABC

is inscribed in a circle with center

U

and radius

r

. A tangent

c'

to a larger circle

K(U, 2r)

is drawn so that C lies between the lines

c = AB

and

C'

. Lines

a'

and

b'

are analogously defined. The triangle formed by

a', b', c'

is denoted

A'B'C'

. Prove that the three lines, joining the midpoints of pairs of parallel sides of the two triangles, have a common point.

Problem Statement