6. In Triangle ABC, the circumcenter and orthocenter are collinear with vertex A. Which of the following statements must be true?
(1) Traingle ABC must be an isosceles triangle.
(2) Traingle ABC must be an equilateral triangle.
(3) Traingle ABC must be a right triangle.
(4) Traingle ABC must be an isosceles right triangle.
Enter your answer as a comma-separated list. If there is no correct option, write "none".
7. Let H be the orthocenter of the equilateral triangle ABC. We know the distance between the orthocenters of Traingle AHC and Triangle BHC is 12. What is the distance between the circumcenters of Triangle AHC and Triangle BHC?
8. As shown in the diagram, points B and D are on different sides of line AC. We know that Angle B= 2*Angle D=60 Degrees and that AC=4sqrt(3) . What is the distance between the circumcenters of Triangle ABC and Triangle ADC?
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