_{1}and Γ

_{2}be arbitrary circles that intersect at points P and Q.

Prove or disprove that there exist points M and N such that

(1) M ∈ Γ

_{1}\{P,Q},

(2) N ∈ Γ

_{2}\{P,Q},

(3) M, N, and P are collinear, and

(4) ∠MQP = ∠NQP.

If they exist, prove or disprove that they can be constructed with

straightedge and compass.

Here is a link to Wolfram MathWorld:

Definition of Set Difference