Let A1, A2, A3, and A4 be distinct points on a circle Γ. Let m
be any line in the plane of Γ such that m does not contain any
of the A's and intersects lines A1A2, A2A3, A3A4, and A4A1.
Let Pi = m ∩ line AiAi+1 for i = 1, 2, 3, and 4 ( with A5 = A1 ).
Let B1 be a point on Γ distinct from A1 and line m. Let line BiPi
intersect Γ again at point Bi+1 for i = 1, 2, and 3.

Prove that line B4P4

intersects Γ again at point B1.

No solution yet.

The problem would have been more easily read if the
last four lines were replaced with

"Let line B_iP_i intersect Gamma again at point B_(i+1)
for i = 1, 2, 3, and 4. Prove that B_5 = B_1."

Note: If you do an inversion with respect to the
circle Gamma, then all the lines ( not through the
center ) are inverted into circles through the center
of Gamma.

Posted by Bractals on 2015-07-02 16:42:45